1 Master of the Arts: Only thing that realy matters here is the skill level of the person. I don't think there is any consequance of having low relations with your masters.
2.Kokujin and Daimyo:
Using family members pro:
-bonus relation is realy nice
-they will not plot against you
Using family members con:
-they can become pretenders for the clan leadership, wich can lead to a civil war
-sometimes there are not enough family members, expecially early on
Using non-family members pro:
-no civil war
Using non-family members con:
-they can take part in plots against you
-relations will be lower then with family members
Overall:
I would always use family members if possible because the biggest con can be easily disabled. If you make sure that your nominated heir has enough land then the others won't vote against him(or at least its lot less likely).
Daimyo titles:
-I like to keep the rule that only family members can become daimyo. Daimyo can have any number of vassals so they can become realy powerfull. So its safer the have a family member in that position.
-if you run out of family members and need to hand out more titles make sure not to give any to people with the "ambitious" trait. People with "content" trait are best choice.
4.Submission of other clan leaders:
-Don't do it unless realy necesary, or you are at a point where nothing will stop you anyway. A subject clan leader can have any number of vassals including daimyo so its possible for them to grow realy powerfull(and they can plot against you!). As discussed at the daimyo part above, its not a good idea.
-Also keep in mind that the subjugated leader will hate you.
-Sometimes its ok to subjugate instead of finishing the conquest to exploit an opportunity elswhere. ( like your other neighbour is in a sudden civil war and you wan't to join it)
EDIT: to respond to Hister's quetsion:
What do you mean by "submission of enemy clan leaders"? Don't they become kokujins when they agree to be subjugated?
Nope they become subjugated "leaders" who can have kokujin or daimyo vassals of their own.