Yes, central government is moving to withdraw all central funding from councils. Local councils are now supposed to rely solely on local funds to supply all services. So local business tax, and council tax. That is why you are getting cuts and higher local taxes.
Spot on. The revenue support grant from central government used to account for over 80% of local government spending, it is being reduced to zero. Councils are very limited in what they can cut: education spending is mostly devolved to schools under a formula, and the cost of adult social care is rising exponentially. These are the 2 biggest council expenses.
Councils can only cut services where the law doesn't specify the level at which the service must be provided. That's why things like libraries are so vulnerable: the statutory level is "comprehensive and efficient" and what that means isn't defined in the legislation, ditto waste collection and highway maintenance.
In areas where property values are low, the rise will be disproportionately greater. Band D tax is 100% of the average, band A 67% and band H 200%. Given that 1991 valuations are still being used, there are probably authorities where there aren't any properties above band A, so that 67% has to be 100%. And to add to this joy, about 4-5 years ago the government abolished council tax benefit, leaving councils to set up their own schemes. Some didn't, and most schemes are less generous than CTB was (even the poorest have to pay 20% where I live).
The district council where I live has the dubious distinction of having been in the top 10 most expensive areas for years, and for a few years was the highest in the country. We pay £1,828 for a band C property. Our roads are so bad that you can tell when you enter the county, but we still get weekly bin collections. We have to buy our own bins though!
Local income tax seems like an attractive option, but the people who get away with making loads of money and hardly paying any income tax would get off lightly again. The tax take is not predictable - an area that suffered big job losses would lose a lot of income. A property based tax is much easier to collect - houses don't move and disappear. A local income tax would increase the pressure on the "just about managing" wage slaves.
TL,DR - it's the government's fault.