Right, let's take this one step at a time. First the technical stuff. I haven't done enough webdevelopment lately to really comment on the standard compliance of IE9 and firefox, although the sources I did find seem to indicate that firefox is still better (for example,
http://arstechnica.com/open-source/news/2011/02/mozillas-modern-browser-attack-on-ie-overlooks-firefox-shortcomings.ars, it also shows the subjectivity of the matter). I know in the past IE was definitely more lenient with standards and let you get away with crappy coding, i.e. your code wasn't totally standard compliant, but it worked in IE anyway, while firefox for example would not accept it. And it remains difficult to judge your sources, perhaps the guy saying his "standard compliant" code doesn't work in firefox just didn't understand the standards fully and did something wrong. Or maybe those that praise firefox' standard compliance just don't test thoroughly enough.
Anyhow, I don't think browser support is really a choice. If you don't want to annoy a significant portion of your players you will have to support IE, firefox and chrome at the very least. The only thing you may assume is that they use the latest version of such browsers.
That said, I use firefox and had little issues. The cursor did disappear although wasn't locked to the game as I would've expected (although I don't know if this was actually supposed to happen). Btw, I don't know what issue you had with firefox, but I see you use JS to hide the cursor, what also worked for me (in firefox) was to use the CSS style cursor:none for the image (for example adding style="cursor:none" to the img tag). As for the sound issue I personally would go for a dynamic switch between ogg/mp3 depending on the browser (but more on the actual sound later :P).
Now for your first question, would a game benefit from these type of interactions?
I'm having difficulty coming up with a straight answer. On the one hand I want to say, yes, it's the way forward. Combining the interactive animations from the games of Shark and Pusooy (which have been very linear) with the dating genre (which focus more on branching, non-linear stories) seems like a logical step. On the other hand, I'm very weary about this. One reason in particular is that I haven't found animations to add much to the dating games. Or in the case of IllustratedLoveStories, where you can't skip the sometimes lenghty animations, I found it interrupting the flow of the game.
I think a large part of it comes down to whether the animation adds to the game. For me personally, if you're gonna add animations of the type "wiggle 10 times with your mouse to fill a pleasure bar" (like leonizer's games), then you're better off with just a fixed animation or no animation at all. But if you start using concepts like in your later tests, where you can imagine a possibility of either failure (not being gentle) or added success (doing something special, having good/consistent timing, reacting to her desires, etc.), then it might actually add to the game. Both can easily fit into the dating scenarios: Not being gentle when asked is a strong negative, the sex scene either stops or shortens, any successive dates the girl will be more reluctant. On the other hand doing something special can unlock bonus scenes.
However, I think it's important to keep in mind that you're mixing genres. Pusooy's and Sharks games work because they're consistent in the speed of interaction and the type of challenge they require. I think the linearity of the games is mostly due to the amount of work required, but it also makes sure the slow interactions are not a burden. An example where this did become a burden is HA3 (if I remember correctly), where you had a fairly long (multiple scenes) linear start with a 3-way choice at the very end. That choice required replaying the linear bit 3 times to see all content, and since that content was all static it's 3 times doing the same thing, and actually waiting on the progress bars (when you do it the first time, it doesn't feel like waiting, any repetition will). What I mean to point out with this is that adding non-linearity will cause players to replay content. In dating games many of these situations can either just be clicked through quickly (I can probably still optimally click through the intro of Dating Ariane...), or will have choices involved that can change the further game. In an interactive animation neither may be the case, unless you specifically keep it in mind while designing it. I would find it annoying if I'm looking for a specific ending, trying out different combinations in the dating aspect of the game, to have to wait for say a 10 second interactive animation that I have done before and has no impact on the game.
Another issue that may arise is that the game may not feel as a whole. For example, Pusooy's cut-scenes involve smooth transitions from the story bits to the interactive bits, it feels as one continuous story, even though in the story bits the characters are not necessarily animated. I think that putting interactive scenes like these in a dating game, as a replacement for an image with choices, may detract from the game feeling as a continuous story (like, suddenly things are moving and animated, while at other times the interactions are discrete (i.e. you click and the image changes)). In the same way you couldn't take one of Goblinboys (or any AIF) games and add point and click gameplay to the graphics without it being out of place. Perhaps integrating scenes like these may require a shift towards Pusooy's style altogether, by leading the rest of the game up to the animations, keeping it in the same style, etc.
If I'm totally honest I imagined "the way forward" more along the lines of Pusooy/Shark adopting non-linearity (Sharks 'Babysitting' was a nice step in the right direction) than dating games exchanging their primitive animated sex scenes for interactive ones. I think part of this is because these interactions are hard to get it right. For example I wasn't able to perform the action in Test 6 consistently. I got it right a few times, but that felt more like luck than anything else. In this case having the cursor visible, or having some other visual cue, may actually help.
But back to the point, considering the effort required to make these animations (take the development time of Sharks and Pusooy's games as an indicator), you may consider whether it adds enough to a dating game to be worth it.
Finally this leaves me with the matter of sounds (I feel like I'm going all over the place with this post... :P). Besides the technical issues, there have been a few games that tried to add sounds by using a sparse "oh" sound. This never seemed any good to me, an "oh" in the middle of otherwise silent gameplay is just gonna be out of place. If you do sound, do it right, don't just add moaning, also add sex sounds, make sure it isn't repetitive, etc.
Oh (pun intended), and please don't use over-the-top loud moaning from porn. That sort of stuff is one of the things that keeps me away most porn in the first place. Some soft moans or heavy breathing are much more arousing in my opinion.
</long post which took way too long to write :P>