Also since I got my spouse visa almost 2 years ago, I've not been in a stable job, my partner who is British earns almost 19,000 pounds annually and we live in a private rented house. We owe council tax but paying what we could afford every month, my partner also claim housing benefit. Could me not being in a stable job, my partner claiming housing benefit and the council tax issue affect my application?
If you're under the old rules, and you can show you are paying off your council tax, then no, it shouldn't affect you.
There's no official minimum income requirement for ILR under the old visa rules, and I have never seen an ILR refused due to finances, even if neither partner is working and they are living entirely off the UK citizen's benefits.
All you have to show for ILR is that you have 'enough' money to live off without the non-UK citizen needing to claim public funds. They generally define 'enough' money as having at least the same amount left over after paying rent and council tax as a UK couple (plus any children) would receive in income support every week.
This amount is £113.70 per week for the couple plus £66.33 per child (£492.70 (couple) + £287.43 (per child) per month) after paying your rent and council tax, but before any other expenses.
This is the same income requirement you needed to meet for your spousal visa, so if you can still meet it, you will be fine.
So, if your husband earns £19,000 per year, you just need to deduct your monthly rent and council tax from it, and see how much is left over. You can also include your savings if you have any (dividing them up between a certain number of months). If you are able to show at least the income support amount, you should be fine.