What do the character components in 旅 and 派 represent?
though part of the right component of the character "旅" &amp; "派" look similar, they've different origin.

旅 (u+65c5) is a character since oracle bone script, that it's composed by 㫃 (u+3ac3), plus 2 人 (u+4eba)

旅 (u+65c5) in oracle bone script:


㫃 (u+3ac3) in oracle bone script:


人 in oracle bone script:


then, the character 派 (u+6d3e), according to 說文解字 is 水 (u+6c34) +  (u+200a2), in which  is the mirror writing of  the character 永 (u+6c38).

永 (u+6c38) in oracle bone script:


flip it horizontally, you've  (u+200a2):


so, about your question:

what does that bottom left character component 
in these two characters represent?


㫃 (u+3ac3) roughly is a flying flag. while 水 (u+6c34) is water.

What about the top right part of 旅?


the character 旅 (u+65c5) should be "chopped" into 㫃 + 人, if not, you'd be confused.

to look up all the characters in Chinese that have
one of these two non-radical components in them


the components of chinese characters ranged from 1600+ to 3000+, depends on who did the research, including simplified chinese, oracle bone script, bronze script, small seal script or not.

though i don't have a smartphone yet, it's in doubt that any apps in android, or ios would satisfy your need.

lastly, i would recommend multi-function chinese character database to you, which is "with archaic script forms, etymologies, english-chinese lookup, &amp; word-formations phonologically disambiguated according to the cantonese dialect"

have fun :)