Multiple DHCP servers in one VLAN is possible. There can be operational issues if they are not under the same administrative control.
Usually there are more than one DHCP servers per VLAN for redundancy. Considerations need to be made to avoid DHCP conflicts. If DHCP servers share the same DHCP pool, something needs to be implemented to make sure the DHCP server does not offer an ip address that's already in use.
One approach is to use DNS forwarder on the access VLAN, the forwarder forward DHCP packets between hosts and DHCP server cluster. The DHCP server cluster are stateful (knowing which ip addresses have already been assigned).
Another approach is to use DHCP options to distinguish clients. For example, one DHCP server works for IP phones and they only offer IP addresses when certain DHCP options are set in the client's DHCP discover. This DHCP server uses a dedicated pool.
The short answer is, yes (as long as they are properly configured)
VLAN is a layer 2 concept. A VLAN separates layer 2 broadcast domain.
You can think of a non-managed switch as a switch with all ports in one VLAN. (no VLAN support is effectively every port in one VLAN).
You can have two hosts in 192.168.0.0/24 and 2 hosts in 172.16.0.1/24 connected to the switch. Hosts in the same subnet can directly communicate with each other through the switch.
The problem with this approach is that everything is in the same broadcast domain. Packets destinated 255.255.255.255 will be sent to every port in the VLAN, which may be a security issue, a waste of bandwidth, processing power etc.
Even if you assign each port into their own VLAN, multiple subnets can still exist on one port (multiple IP addresses on one NIC, secondary IP addresses etc.).