VLAN - Network Redundancy With Same 2nd Switch?

Solution 1:

Is it possible to set up the same VLANs on two different switches

Yes, just make sure you trunk the VLANs to both switches (using 802.1Q tagging), see below.

with same IPs, but different MACs

Yes - if you're using different MACs, the failover isn't actually up to the switches but the hosts. Switches only care for MAC addresses and as long any of those isn't visible on different switch ports they'll be fine.

on dual port network cards of servers?

What you're looking for is called NIC teaming with one port active and the other in standby, in case the active port loses its link. Most dual-port NICs support teaming but that may also be up to the server's operating system.

Likely, you'd not only want to make the switch redundant but also the individual server links, which requires connecting the switches with a VLAN trunk.

If you can't tolerate a redunction in overall bandwidth, you may need to make sure that the link between the switches is fast enough to handle your workloads, in case traffic splits across the switches - one or more ports going down with some servers failing over. Commonly, a dual, aggregated link is used (which also handles a single link failure at that place).