1. You didn't post where you are in residency at the moment, but generally you want to start looking for a job around ~november or so of 3rd year. Getting through the credentialing process to get staff privileges can take up to 3 months at some hospitals, so you want a job offering ASAP - you dont want to get an offer in june and not be able to start for 3+ months. If you plan to take IM boards you would take it around this time as well.
2. Tricky question, and definitely depends on the position. I guarantee you any program WILL attempt to determine whether you want a position for a year or two or are looking for something long term. Although it is still doable, finding short term positions is becoming increasingly more difficult as more people enter hospital medicine.
3. I can't imagine any program ever asking about your procedure log. In general they would expect some competency with core IM procedures. The amount of procedural work also varies INCREDIBLY between positions. I've been an attending for 5 years, and in 2 different jobs I've had to do a total of 0 central lines myself. I've supervised maybe a half dozen lines with residents. I've done a fair amount of thora's, para's, and LP's but even those I don't do any more since we established an inpatient procedure service at my current job. my last job the IR department (since it was at a private hospital) would literally jump at the chance to do any procedure so I didn't ever need to bother doing them myself. I did discuss one position over the phone with one director and they were all doing their own swans and intubations - things I barely had to do as a resident and certainly did not want to be doing all the time as an attending.
When you need to get a DEA as a resident varies between programs I think. I was at a county program so did not need my own DEA as a resident, but I thought most needed it earlier? Regardless, you absolutely CAN NOT work as an attending without a DEA #, so you definitely want to get it taken care of.
I'm not entirely sure what you can do to make yourself look like a stronger candidate for a short term position since those people we often try to weed out. Although I guarantee if you wanted to be a nocturnist for a year I'm sure some program would love that. =p