I'm trying to learn Irish just for fun, and the grammar's REALLY messing me up. Any tips?
You're doing the right thing by asking and not just plowing blindly on! There are some really helpful people here who will do their best to explain things--just try to be specific in your questions. Another helpful thing is to read the grammar notes provided with the lessons and maybe print them out for reference. Good luck!
Edit: Apparently my information was wrong. It still might help you remember how it works, though, so you can check it out.
Based on you being level 2, I'm guessing that you haven't actually come across verb conjugation yet. What you're probably seeing is, for instance, tá becoming táim or táimid. These aren't conjugations, they're contractions - just like the words aren't and they're. Táim comes from tá mé, meaning I am, and táimid comes from tá muid, meaning we are.
In other verbs, like itheann, things are contracted a little more, so you get ithim and ithimid, but it's still the same basic system. All other nouns take the form itheann. Also, you are allowed to say tá mé and tá muid instead of táim and táimid. The contractions have to do with different dialects of Irish, IIRC, and either way is officially correct and will be understood.
Basically, táim is I'm, and ta mé is I am. The distinction isn't exactly the same as in English, but the point is that they mean the same thing and one was formed out of the other basically the same way.
They're not contractions. They're different conjugation patterns based on dialectal differences. Some dialects (Munster) still use mostly synthetic forms, similar to Spanish. This is where the ones like Táím and Táimid come from. You'll also hear non-standard things such as tair or taoi (tá tú) or táid or tádar (tá sibh). This continues into the other tenses as well (bhíos, bhís, etc. for past and bead, beir, etc for future). It's not a contraction, but a totally different conjugation scheme.
They don't function like contractions in English do, however. There's times in English when, even if you normally say "I'm", you'll use "I am." In Irish, it's consistent throughout the dialect (for non-learners). You'll either use synthetic forms, or analytic forms, except in a few cases, mostly dealing with the first-person singular, though even that is usually fairly consistent and is based more upon them dying out in dialects vs. what's taught in school.
You'll never hear a native speaker say something like Tá mé go maith; táim ag dul go Báile Átha Cliath inniu. It'll be Táim go maith; táim ag dul go Báile Átha Cliath inniu or Tá mé go maith; ta mé ag dul go Báile Átha Cliath inniu.
The best Irish grammars in English I've come across are the ones by Nancy Stenson ("Basic Irish: A Grammar and Workbook" and "Intermediate Irish: A Grammar and Workbook".) They aren't cheap ($40 or so the last I looked) but the explanations are the clearest I've seen and the exercises are excellent. You can find lots of other resources online too. You might try the Daltaí na Gaeilge site (http://www.daltai.com). They have some pretty good grammar examples.
I'm a grammar nut. It's how I approach a language, but for some people it works better to not worry about the "whys" and just experience the language. Over time the "rules" (which are just approximations of what is happening in a living, evolving language) start to bubble up to your consciousness. Guess it depends on what kind of a learner you are.
Ar aon nós, don't give up! It really does start to come together over time.
Lenition doesn't actually feminize words. It is used after 'an' to show that a word is (by its own nature) feminine. There are 17 uses listed here: http://www.nualeargais.ie/gnag/gram.htm You probably won't understand all of them yet; don't worry about that!
You know that only b, c, d, f, g, m, p, s*, and t can be lenited. (Except sc, sm, sp, st--Scallions smell spicy in stew--and the less common sf)
You may know that some tenses (like the past) are lenited. You may know that the possessives mo, do, and a (when it means 'his') cause lenition. You may know that certain prepositions cause lenition. You may know that preposition + an always causes lenition in Ulster Irish You may know that there is lenition in the vocative case. (A Sheáin!) You may know that you lenite nouns after numbers 1-6. The rest you can get from the list I linked to.
Also--you do need a book like Gaeilge Gan Stró or even a simple grammar book like Progress in Irish.if you plan o learn the language. Unfortunately, Duolingo doesn't always do a great job of explaining grammar.