Direct answers to your questions are either not possible without more information or might not really help you. I'll try to explain:
The maximum transfer unit is the largest IP packet size that can be sent on a given interface. With Ethernet, the MTU is generally 1500 bytes.
Ethernet's maximum frame size is 1518 bytes for untagged standard frames - 18 bytes is the overhead for the smallest Ethernet header + FCS, 1518 - 18 = 1500 bytes payload. If you tag 802.1Q VLANs the header increases to 22 bytes, with a maximum frame size of 1522 bytes. QinQ adds another 4 bytes and so on.
When tunneling, you encapsulate either an Ethernet frame (L2 tunneling) or an IP packet (L3) into an outer IP packet. If you need to use the standard Ethernet MTU even inside the tunnel, the outer packet and frame need to grow accordingly.
In reverse, if the outer packet/frame cannot increase (e.g. across the Internet) the inner packet/frame cannot use the normal maximum size.
L3 tunneling requires an additional IP header, so the MTU needs to be 20 byte less (with IPv4) than the normal 1500 bytes (assuming the path supports that). L2 tunneling over IP requires both an Ethernet and an IP header, so it eats away 38 bytes from the standard MTU.
Sending a (standard) maximum-sized packet over a tunnel with decreased MTU requires fragmentation either by the router, or (preferrably) by the source using path MTU discovery (PMTUD).
Fragmentation increases processing overhead (in routers) and wastes bandwidth (for the additional fragments' headers), so it's good to avoid.
In some scenarios it might even be reasonable to reduce the MTU/frame size across the whole network, e.g. for a remote location that uses a VPN tunnel for everything anyway, removing the need for PMTUD or router fragmentation.
So, when examining which MTU is the best in your case, you need to find out the maximum packet/frame size for each tunnel you use. In most cases there is no strict standard but you have to consult your ISP.
Jumbo frames - Ethernet frames with a payload larger than 1500 bytes - can be useful when accommodating tunnel overhead in order to avoid fragmentation ("small" or "baby jumbos". However, frames sizes are not negotiated and need to be configured alike across all nodes in a given segment. Nodes configured with a smaller maximum frame size than others (=MTU mismatch) will drop 'oversized' frames. You should restrict jumbo usage for special purpose links and not use them lightly. So yes, OSPF and BGP can both fail if frames cannot be received properly.
Large jumbo frames - usually with 9000 bytes MTU - are only used on high-performance networks to decrease overhead. Most NICs support offloading features that - more or less - make messing with jumbos unnecessary.