Lots of different questions!
The key with variable income (or annual expenses), is to use the money that comes in THIS month, to use for NEXT month's spending. If you don't have as much income as intended, you have another 2-3 weeks to reduce your future spending and accommodate it.
For lumpy expenses, you need to pay yourself first out of your budget. Have those amounts taken off the top of NEXT month's budget and put aside.
Only you can decide if you will pre save for renovations, take a loan, save for retirement, etc. First ensure that you have at least 6 months of basic monthly expenses set aside, due to your income fluctuations.
I love this. I understand YNAB works this way, so that might be an effective tool to implement this.
When I was working on a project basis, the only way we made it work was to base our minimum "required" standard-of-living expenses on our minimum monthly income. [side note: I would strongly suggest using YNAB or some other method to track what you spend to make sure that what you say you spend is actually what you spend - it's super easy to go over without noticing, and if it's a low month, you can't afford that.]
After that, you just need to decide what to allocate to the extra, and in what order. E.g., first extra $100 to vacation fund, next $250 to renovation fund, next $50 to extra lifestyle fund, then another $100 to vacation fund, the, $500 to renovation, etc. You can layer it this way so that you can make progress on multiple goals, but always putting the most of the extra into your higher-priority goals. [second side note: I intentionally put "extra lifestyle" in here so that you can reduce your base budget to real bare-bones, but then in good months allow yourself a little extra -- a restaurant meal, a movie, whatever the thing is that floats your boat -- so you don't feel deprived all the time. Because otherwise those things tend to creep into your base budget, and then, boom, you don't know where the money went]
Or you can just sit down each month and decide how much you want to put to each goal. That works too, if you want to revisit and discuss more frequently [me, I like to decide once and then not have to worry about it, but YMMV]. Or you can just dump all the extra into one big savings account and decide later how much you want to spend on vacation vs. reno -- it may feel more encouraging to see one number grow faster vs. watching separate pots grow. Or do something in-between -- we used to combine "known longer-term recurring expenses" (e.g., car fund, vacation) in a separate pot than one-time things like renovations, just because of how my brain works (I wouldn't spend on the big thing if I worried I was taking money from other known future needs -- totally illogical because we had budgeted for everything, so it wasn't like the cash wasn't there, but I have found that life is a lot easier when you work with your quirks instead of trying to fix them).
