As Jessi said, I think this is a really good idea! I know I used to have problems with several of the words you mentioned. Just to quickly go over a few...
tell: 教える vs. 知らせる vs. 言う
Broadly, 知らせる is used in more formal instances. For example, お知らせ (Notice) is equivalent to one of those 'Attention' or 'Information' signs you'd see at the station or in a shop, etc.
教える as you know is literally 'teach', but this is the one you will hear most often in the sense of 'tell someone something', eg. 今週のスケジュールを彼女に教えてもらった (She told me/I had her tell me the schedule for this week).
言う is just 'say', and has no overtones of 'telling' or 'teaching' someone anything - 彼は火曜日だと言ったけど、私は違うと思う (He said it was (on) Tuesday, but I think that's wrong).
hard to: ～にくい vs. ～がたい vs. ～づらい
～にくい is most commonly used in both casual & polite speech. 分かりにくい (hard to understand), 食べにくい (hard to eat).
～がたい is basically the more formal or written form of ～にくい - you'll often hear it in court trials, political speeches etc. 理解しがたい (difficult to understand).
～づらい ... personally I use this interchangeably with ～にくい (I'd like to confirm this with a native speaker, though!). The only thing I can say is that ～づらい sounds 'slangier'. I wouldn't say it in keigo.
do: する vs. やる
やる often has the overtone of 'trying' to do something, as in 'giving it a go' in English （やってみます）. You may be aware that やる has a sexual secondary meaning, too. Basically, don't use やる in formal/polite situations; even やります isn't great. It can sound sloppy at best and rough and slangy at worst. If in doubt, go for する！
how/why: どうして vs. どうやって vs. なんで vs. なぜ vs. どう vs. どのように
GREAT question, this one!
どうして is 'why', a polite version. (どうしてそこに行くの？Why are you going there?)
なんで is also 'why', but a slangier/more casual version. (なんでそんなこと聞くの？
Why are you asking me such a question?)
なぜ is the most polite and formal version of 'why'. （それはなぜですか？ Why is that [may I ask]?) It can be used on its own in casual conversation, though - just なぜ？ Why?
どうやって is literally 'how to do (something)' and means 'how'. It's very casual. (どうやって実家に帰るの？ How are you going back home [your 'real home'/parents' house]?) どういう風に is the 'polite' version of どうやって.
どう literally means 'how' or 'in what way', and can be used in a number of ways. どういうこと, for example, is used often as an interjection to mean 'What do you mean?!'
And finally, because I really thought this was also a great question...
love: 愛 vs. 愛情 vs. 恋 vs. 恋愛 vs. ラブラブ
愛 is the equivalent of 'Love' (capital L) in English. As in 'Love is a many splendoured thing'. Used when talking about love in general. Not used lightly in conversation about real people - 大好き is much more common to express 'I love him/her', if indeed you get on to such topics at all. 愛している is only said in private to the object of one's affection... and I read a survey fairly recently that said a vast majority of Japanese men had never uttered these words in their entire life 笑！
愛情 is the -feeling- or emotion of love and/or affection for another person.
恋 is, to my mind, a 'lighter' version of 愛, in the sense that it often has overtones of youth and passion as well as innocence and 'first love'. It crops up a lot in manga for girls! 恋に落ちる is 'to fall in love'.
恋愛 is often used in phrases such as 恋愛経験 ('love experience', meaning one's romantic history). It can also be used as a verb （恋愛する・恋愛している）to describe 'being in love' or 'being in a (love) relationship'.
Of course, a lot of these are based on my personal experience and opinions, so there may be some differing opinions out there, but I hope that helped a bit!