You dont explain, are you going for the job or conducting interviews for a DBA for your team? re 1 - DBA daily activities change depending on the place of work but I would expect to have someone mention, backups, scheduled jobs, check reports on HDD space;error logs, etc re 2 - I have no idea what you mean. please rephrase it as a question.
I have to agree with @Fatherjack and @GrantFritchey on (1). Backups, job completion, disk space, etc are all the basic day to day task that every DBA should be doing. If I have to guess as to what your second question might be is that you are wanting to know two things to do if you are having performance issues on a server. Well that really depends on what the symptoms are. If you are having users complaining about things being slow then first look for blocking, then start looking for I/O issues with CPU, Memory, or Disk. Hope this helps.
As to #1, I will start by echoing FatherJack and Grant. Backups, job completion, monitoring basic stats are all vital and daily. But one thing I would like to add to that list is communicating with others. Being able to receive requests from other people, prioritize them, and provide status reports is almost as important as being able to handle the technical side, and at least in the organizations I have worked in as a DBA (for disclosure, they have all either been small companies or else a small nearly independent project inside a large company) this was a daily activity for a DBA. As to #2, I will also agree that I am not entirely certain what you are looking for. What I think you might be asking is along the lines of "How do handle performance problems in your server?" If that is the case, then the answer would involve steps like: 1. Check to see where the problem really is. Sometimes problems blamed on SQL are actually inside the application using SQL, network congestion, or even something else using up all the resources on the end client. 2. Checking for other, non-sql programs running on the system that might be degrading performance. 3. Further optimize the code. 4. Further optimize indexes and make sure associated statistics are up to date. Etc. I wrote a broad overview of things to look for at [
http://www.sqlservercentral.com/articles/Performance/71001/] and Gail Shaw has one far better than mine at [