The first one is not a problem at all, or at least, it's a good problem to have. When random thoughts pop up uncontrollably it's a good sign you are getting very close to sleep. At which point you should simply let go and fall asleep as quickly as possible. You shouldn't try to control your thoughts as that will cause you to become tense and may not be able to fall into sleep. The beauty of SSILD, compared to other methods, is the "lazy" approach -- no need to concentrate and no need to stay still. The only problem you may have with this is that you may not have warmed up sufficiently for SSILD to work if you fall asleep too quickly. To counter this problem I suggest you either stay awake a bit longer before returning to bed, or get more sleep prior to performing the exercise. Both options are better than trying to force it during the exercise.

As for the second problem... sometimes we walk a very fine line between sleep and awakened states. This is especially true with the subsequent awakenings resulted from SSILD. Many of these awakenings are FAs, but some may turn out to be an intermediate state which can be easily transformed to either sleep or waking state in an almost seamless fashion. Once you learn how to utilize this state you are guaranteed to achieve near 100% success rate with SSILD.