Vetra

All the tournaments in the Tournaments section are held on simulators, and all the tournaments in the Wi-Fi Tournaments section are held on wifi, so you have quite a choice. :) Unfortunately you'll be at a competitive disadvantage if you use Pokémon that aren't specially bred to have optimum IVs, especially without the ideal Speed and the lack of Hidden Powers, but there's nothing to stop you from raising them. If you do resort to using PokéSav, please keep in mind the Wi-Fi forum rules, which are very specific as to how you're allowed to use PokéSav and what disclosure is required. ^_^

Alright, I'm glad to hear it! Unfortunately Generation 4 (my favourite gen :P) isn't as popular as Generation 5 anymore, but there are still Generation 4 tournaments in the Tournaments section occasionally, and if you're willing to be patient, waiting a little while on the bigger Pokémon Online servers might yield you an opponent. Hopefully Pokémon Showdown! will support HGSS in the near future.

Sorry I had to lock your thread, but I hope that my reply was able to answer some of your questions! If you need any more help navigating the site/forums, send me a private message or leave a note on my profile, or try PMing the moderators of the respective sections. I'm happy to give as much assistance as I am able, though I'm not involved with the Battling 101 program.