DH and I were foster carers alongside having 2 young DC of our own. Our experience of the assessments were not at all awkward in terms of personal questions, it really doesn't get highly personal. Personal references are taken up, and risk assessments of your home undertaken. There is training to attend - which is paid, or at least expenses covered.
Councils desperately need more foster carers, and imo especially more who are experienced at caring for young children, so I'm sure they would love someone with childminding experience.
Whether they would allow you to actively be childminding at the same time as fostering I am unsure. The foster dc often have very complex needs, and being looked after alongside other DC can be difficult for them, especially if there a lot of others, who change regularly.
Another consideration is whether your mindees parents would be happy with them being looked after alongside foster children. We stopped fostering because of a foster child's treatment of our DD1, and although we plan to do it again in the future, I wouldn't be happy with my DC and foster kids being looked after together without me around. There are some very damaged foster children.
If I were you I would approach your coucil. A very friendly social worker will come out to meet you and chat over potential options. Depending on the ages and what kind of fostering you are interested in, it may be possible to work it around child minding, they will be able to advise. The money you would get from fostering would be higher ime than childminding money. If you don't want to take it any further, then it will be easy to say so. If it any point the process becomes too intrusive then you can pull out at that point; we were worried about that aspect but needn't have been. And if you decide to go ahead it tends to taken at least 6 months, so there is nothing to lose by starting the process at least.
There are lots of types of foster care; long term care, respite care (while long term foster carers are away on holiday or ill), emergency care (DC just taken from their unsuitable situation... this is probably the hardest work), respite/day care of disabled DC who live with their families (usually dealt with by a different department) and more.
Some local authorities are better than others about how supportive they are of you. We didn't have any problems with lack of support, but that's because we were fairly demanding and tough with social services when we needed to be.
I highly recommend fostering - but at the same time I acknowledge that it is incredibly hard emotionally at times, and there is a lot that the government need to do to improve the situation for children in care.