I'm guessing fitness is started at the gym and chemistry is grinded at the lab classroom at the school after unlocking it? Any other skills?
fitness and appearance can be grinded in the fitness room (or at home if you buy a weight set + jogging can be done in the woods near the park), chimistry in lab + book you find there, lockpicking can be "Unlocked" when reading ther newspaper you find in the restaurant. afterwards talk to ms hooter and she will tell ya that there are burglars on the street lockpicking homes. now go to the park and witness a pickpocket doing his job. confront him and demand to show ya his tricks. now you can lockpick too. lockpicks can be bought in the security shop and can be used to lockpick locks to get into houses. the only way to train is to simply lockpick doors (in the past you could ask the thief to train ya, but that seems to be removed).
hypnosis can be unlocked and trained when you go to the detective and look into his drawer. read the book several times then reutnr to the detective. get ya lessons from him 'til you are confident enough to do it on ya own. at any time though /after reading the book at least once) you can try to hypnotize people on the streets and train that skill that way.
another skill is the suggestion. once you hypnotized someone you can tell 'em what to do. this trains ya suggestion. you can't use the same option several times though as it can train ya suggestion only once. if you used up all ya options on one person to train ya suggestion, find a different person and do the same shit.
hacking is also a thing here. you can train it by buying a pc at the scurity shop, install it in ya living room and hack some websites. you can also hire that librarian, flirt with her a bit and get ya training from her. hacking is important to corrupt ms underwood and your sister anette.
last but not least, photoshopping. like hacking you can train it on ya pc. you can also train it in ya school if you have a computer room. it's only important for the newspaper agency quest. for that to trigger, ya gotta read the newspaper (again, it can be found in the restaurant), go to the beach and greet a "well hung" reporter "girl". go back to ya home and let that girl in. she will force ya to fake some pictures of politicians. do that, give her the photo when she asks for it and don't ask her how she is feeling (gay content there!), instead ask her if its enough. now you are officially hired to do some fake photo assignments for the agency. go to downtown and to the newspaper agency and get ya jobs ^^. you can photoshop pictures, once you have a high enough photoshop skill. you can do that on ya pc or in the computer room. once you are done with a pic, bring it to the agency.
