To 1): Yes, on most CPUs, SHA-256 is about only 40% as fast as MD5.
To 2): I would argue for a different algorithm than MD5 in such a case. I would definitely prefer an algorithm that is considered safe. However, this is more a feeling. Cases where this matters would be rather constructed than realistic, e.g. if your backup system encounters an example case of an attack on an MD5-based certificate, you are likely to have two files in such an example with different data, but identical MD5 checksums. For the rest of the cases, it doesn't matter, because MD5 checksums have a collision (= same checksums for different data) virtually only when provoked intentionally. I'm not an expert on the various hashing (checksum generating) algorithms, so I can not suggest another algorithm. Hence this part of the question is still open. Suggested further reading is Cryptographic Hash Function - File or Data Identifier on Wikipedia. Also further down on that page there is a list of cryptographic hash algorithms.
To 3): MD5 is an algorithm to calculate checksums. A checksum calculated using this algorithm is then called an MD5 checksum.