가끔 and 때때로 are very similar.
가끔 is used when there is some temporal and spatial separation/gap between the events/places. Note that its use is not confined within time.
e.g. 이 길을 따라서 가다 보면 낚시할 만한 곳이 가끔 있어. Along this way, there are some fishing spots. (Implying the spots are not together but separate from one another.)
때로 has two meanings.
1. in some cases; depending on the situation
2. sometimes; occasionally
The distinction between these two meanings is often not necessary.
때때로 means 1 and 2 altogether: from time to time depending on the situation
는 can be used to emphasize an adverb, noun, or ending.
때로는 슬픈 날도 있겠지. There can sometimes be sad days. (때로 [sometimes] is emphasized; implying that it is not that every day is sad or no day is sad but it is that some days are.
-씩 has connotation of repetition.
가끔씩: repeatedly with some temporal or spatial intervals
조금씩: little by little