Rubline covered the oil leak, definitely check the o-ring. I just added a chrome oil filler cap and didn't realize that it needed an o-ring until I noticed oil around the new cap. Checked the old cap and sure enough.
For the hot start issue, the maint. free AGM battery is a must, also you may want to invest in a multimeter and check the r/r and stator wires just to be sure. I had similar problems and started with the battery. That worked fine for about two days and then it decided to not start at all when I stopped at a store about half way to work one morning. After investing in an r/r and with a little help from the folks here I found that the problem was the r/r, I replaced it and no issues since. If it is either the r/r or the battery it could put undue strain on the stator, which is bad news. Check the verses for what to check and where on the r/r and stator wires with the multimeter.
Oh, I forgot to mention, the day that it wouldn't start for me at the store I had the backfire two or three times while trying to get her started. Some of the more technical folks here could probably explain the reason for the backfire, but I'm pretty sure it's related to a weak battery not turning the motor fast enough to ignite the gas leading to excess gas which makes the loud boom once a spark does catch....or something to that effect.
I smile 'cause I don't know what the h*ll is going on.