If you have a 20,000 balance and a 8.75% interest rate, you should be paying between $145 and $150 in interest each month, with the balance going to principal. (0.0875/12=0.007292, and that times 20,000 is 145.83; as interest is compounded daily, it'll be a little higher than that.) If the minimum is below $145, then you are not covering the interest; I suspect that is what is happening here, and they're reporting interest paid that wasn't covered in a prior month (assuming you have some months where you only pay the statement minimum, which is less than the total accrued interest).
Assuming you're in the US (or most other western countries), your loan servicer should be explaining the exact amount each payment that goes to principal and interest. I recommend calling them up and finding out exactly why it's not consistent; what should be happening, assuming you pay more than the amount of interest each month, is the interest should go down (very) slowly each month and the amount paying off principal should go up (also slowly). EG:
January: $146 = Interest, $54 = Principal
February: $145.9 = Interest, $54.1 = Principal
March: $145.8 = Interest, $54.2 = Principal
Etc., until eventually the interest is zero and your loan is paid off. It probably won't go this quickly for this size of loan - you're only paying off a tiny percentage of principal each month, $50/$20000 or 1/400th - so you won't make too much headway at this rate. Even adding another $25 would make a huge difference to the length of the loan and the amount of interest paid, but that's another story.
You will eventually at this rate pay off the loan (at $200 a month for all 12 months); this isn't dissimilar to a 30 year mortgage in terms of percent interest to principal (in fact, it's better!). $50 a month times twelve is $600; 400 payments would take care of it (so a bit over 30 years). However, as you go you pay more principal and less interest, so you will actually pay it off in 15 years if you continue paying $200 a month exactly.
What you may be seeing in your case is a combination of things:
In months you pay less (ie, $100, say), the extra $45 in interest needs to go somewhere. It effectively becomes part of the principal, but from what I've seen that doesn't always happen directly - ie, they account it differently at least for a short time (up to a year, in my experience). This is because of tax laws, if I understand correctly - the amount you pay in interest is tax-deductible, but not the amount of the principal - so it's important for you to have as much called 'interest' as possible. Thus, if you pay $100 this month and $200 next month, that total of $300 is paying ~$290 of interest and $10 of principal, just as if you'd paid it $150 each month.
If you had any penalties, such as for late payments, those come out off the top before interest; they may sometimes take that out as well.
All in all, I strongly suggest having an enforced minimum (on your end) of the interest amount at least; that prevents you from being in a situation where your loan grows. If you can't always hit $200, that's fine; but at least hit $150 every single month. Otherwise you have a never ending cycle of student loan debt that you really don't want to be in.
Separately, on the $1000 payment: As long as you make sure it's not assigned in such a way that the lender only accepts a month's worth at a time (which shouldn't happen, but there are shady lenders), it shouldn't matter what is called 'principal' and what is called 'interest'. The interest won't go up just because you're making a separate payment (it'll go down!). The portion that goes to interest will go to paying off the amount of interest you owe from the time of your last payment, plus any accrued but unpaid interest, plus principal. You won't have the option of not paying that interest, and it doesn't really matter anyway - it's all something you owe and all accruing interest, it only really matters for accounting and taxes. Double check with your lender (on the phone AND on their website, if possible) that overpayments are not penalized and are applied to principal immediately (or within a few days anyway) and you should be fine.