Ey there, welcome!
Now, before I continue I need to stress out that I'm hardly an expert on this subject because I mostly focus myself on still renders. However, I have gained a fair bit of experience over the years. Also: many people are probably going to tell you that Daz Studio isn't the best tool for animations because there are other candidates as well. Honestly: I can't comment on this because Daz Studio is all I've used, and I kinda dislike Blender ;) I can say that DS is most definitely capable.
1. should I use Timeline or aniMate to make it?
Probably both. Keep in mind that aniMate2 is a commercial plugin that is sold separately from Daz Studio. But if you're serious about this then I kinda consider it a must-have. In fact, you should probably also look into the Puppeteer pane as well since that can be useful to morph between poses and then record the move onto the timeline.
See: the timeline pane is an excellent tool to create / record a small animation. For example the nipples on a girls b00bs getting hard or... a guys dick getting overly excited. Let's say we go for the b00bs on a Genesis 8 female model. So what if you want to use this again for another character? That's where aniMate2 can excel because it allows you to save your current animation as a so called aniblock which you can then re-use for others.
Or what about penetration? Maybe you'll want to get some pumping action going, so why not build yourself a frame of a guy using his dick going in and out of the girls vagina, save that as an aniblock which you can then easily re-use multiple times to build yourself a bit of a sex scene... as such I think you'll want to use both.
2. How do I make the collision and deformation of male and female genitalia? Or do I have to control their movement in the animator?
Daz Studio has a collision detection system, but it's very basic and barebone. So when it comes to something as complex as penetration you're probably looking at some manual efforts.
3. How to make the female genitals look like the material of the product cover because they look wet and real, but mine looks dry and fake.
Surface properties, it depends on the figure being used but glossy is usually a good property to look into for this, it's roughly the same approach to get a figure to look sweaty or wet (no, just from water drops ;)).
A good way to start would be to open the Surface pane, enable the surface viewport tool and then select a surface of your figure and check out its properties. Basic key properties to look out for: Glossy Layered weight, Glossy reflectivity & Glossy roughness. Now, I'm kinda in the middle of something at the time of writing, but lessee if this works:
There we go!
Notice how Audrey there looks kinda wet'ish with her b00bs & belly? (this is the "Torso" surface for Genesis 8 within Daz Studio).
For a quick start you'll want to bring the "Glossy roughness" down to, say, 0.20 give or take, after that increase the "Glossy layered weight" to above 0.60 and then you can mess around with "Glossy reflectivity" to make it show more or less.
Now... I focussed on Audrey's belly ("torso") here but keep well in mind that these 'surfaces' apply to every mesh you bring into Daz Studio, including the awesome advanced pussy.
Since you said to be new'ish: the reason you can actually see this glossy reflection in my viewport is because I enabled the so called "Filament" viewport render engine. Check the icon on the left side of the "Perspective view" bar in the upper right corner? Filament is a PBR based render engine which I think you're going to love because.. it can seriously help with making nice animations. At the very least it'll be a lot less taxing than, say, Iray...
Well, there we go, I hope this can give you some ideas!