Yes, you can have as many Fixed Rate ISAs with different providers as you like, as long as you do not deposit more than £20,000 across all your ISA accounts each tax year.
The exception to this is Lifetime ISAs - while you can have more than one open, you can only pay into one Lifetime ISA each tax year, and can only save up to £4,000 each tax year.
Tax treatment depends on individual circumstances and may be subject to change in the future. Must be 18-39 to open a LISA. Ineligible withdrawals may return less than paid in.