Use same DNS name both as host name and subdomain

Yes you can! You also do somethhing similar when making example.com and www.example.com point to an A record. You will have to create the A record on the delegated zone though.

You can combine A and NS records but you can’t combine them with a CNAME record.

Note that the terms “hostname” and “subdomain” are kinda synonymous as you can createA records for www.test(.example.com.) and both wwe and test are considered a subdomain. You’re talking about a delegation of a zone here. And you can both delegate a zone and assign an A record to it (from the delegated zone, as its apex).

If you only want to have records for b.c and a.b.c subdomains are not necessary. It's completely valid to have more sub-levels in one file, for example in zonefile for c you can have

b    IN     A    127.0.0.1
a.b  IN     A    127.0.0.2

If you really want a subdomain b.c first define delegation i c zonefile.

b    IN     NS   ns.with.b.c.zone

the ns.with.b.c.zone can point on the same server, or to hosting provider for example. Is good practice to have at least two DNS server for domain. RFC1912

next define A record for b.c in zonefile for b.c

@    IN     A    127.0.0.2

or

b.c. IN     A    127.0.0.2