Hello tiger2.
1. Correct. To "Check for Problems" button is equivalent to scan. I don't see how there are any other option, since the SCAN button is right in front of you.
2. Yes. Spybot-SD is a AS (anti-spyware). AS and AV's can co-exist. Spybot's real-time protection will not conflict.
3. That is possible. I say this because a AS "cannot" scan for every type of malware/spyware, as it will miss something that other AS scanners might catch. Two AS scanner is recommended because one will catch what the other missed. vice-versa.
You should use one AV and one firewall ONLY! Some user's think that having more than one AV or firewall will give them addition protection. But that is not true as the exact opposite occurs. The Resident Shields of the two AV's will conflict as they try to access the same file at the same time. Thus, resulting conflicts, system slowdowns, and even crashes.
I strongly recommend only one of each. Safe surfing.