1. optical cable offers the most interference free connection, but is not necessarily higher quality. Since all other connectors are analog there is no measurable difference between them. Now certain high end headphones will require more power to run or more resistance. This is where having a good sound card can really help. Most gaming grade headphones are designed around standard audio.
3. With any wireless system a degree of latency will be introduced. A good set will have an almost non existent latency while a terrible set will be noticeable.
#1 is there a "higher quality" audio connection type (35mm. opticle etc)
That's going to depend on the listener. Since I'm half deaf from old age, I'm not likely to notice the clarity or lack of distortion issues you get from a digital audio (optical) connection as opposed to an analog 3.5mm connection. Of course, if your sound system (computer speakers or just PC speakers) do not have an optical input, there's no reason to push for an optical output from your motherboard/sound card.
#2 is there a preferred connection for gaming, like a speed difference
Again, this is more up to your budget and your intended use. For me and my Home Theater PC (HTPC), I made sure that my motherboard had an Optical S/PDIF output and my 5.1 surround sound system had an Optical S/PDIF input. Now I only use my HTPC for watching movies (and yes, my apartment neighbors hate me). Some people will go big and spend thousands of dollars to match their discrete PC audio card with an amplifier and high-end speakers. At the other end of the range, when I had a smaller room, I plugged a $70 set of Logitech X-530 5.1 surround sound speakers into my (at the time) $100 Logitech XTremeMusic Sound Card. Now I use my motherboard's optical out to connect to my $300 Onkyo HTIB 5.1 surround sound (for movies). Again, it all really depends on your budget and your intended usage.
#3 would there be any problems using wireless speakers
I used to have a set of wireless speakers for my non-PC home theater set up and they generally let me down. I could never clear up the static I'd hear from them, but that was close to 10 years ago. I can't say how they perform now.
Bottom line, define a budget and state an intended use. Also figure on the space available. For my small bedroom some years ago, my Logitech 530s were more than sufficient. For my larger apartment living room, I definitely need the Onkyo HTIB for full surround sound.