PICTVRA•GVLIELMI•
BRERETON•MILITIS
HVIVS•DOMI•CODITORIS
I can help a bit with the translation:
The "V"s are actually "u"s, so "PICTVRA" is "Pictura", which means "a painting" as the subject. "Gulielmi" is in the genitive case, so you translate it "of William Brereton". "Militis" is a noun in the genitive case meaning "of soldier", but "huius", which means "this", modifies it, and "domi" means "at home".
So the translation (without "coditoris" because I'm not really sure what that means) is "A Painting of William Brereton of this soldier at home", which can be interpreted as "A Painting of William Brereton, this soldier, at home" because since "Militis Huius" is in the same case as "Gulielmi", it can be an appositive.
"coditoris" looks like a third declension adjective, and its ending signifies that it is in the nominative or genitive case, so it could modify either "picture", "William Brereton", or the "this soldier".
For your third question, if you're asking whether there is there a longer version of "Opitulante Deo", then I can tell you that according to this site, there is:
Opitulante Deo Fari Quoe Sentient
Which is translated as:
God being my helper I will speak what I think.
EDIT:
I think I've made some progress on the last line. I couldn't figure out the first part that has the "AN" with an "o" superscript and "e" subscript but the next part, "AET-SVAE 28" I believe means "28 years old". "SVAE" is actually "suae" which roughly means "of his own" and "AET" is an abbreviation for "aetas", which means "age", and wikipedia says this about it:
Abbreviation of "aetatis"; further abbreviated (and more common): "aet." – e.g.: "aetat" or "aet. 36" = "36 years old".
So I presume this means that the painting was made of William Brereton at age 28, since the translation for the last line is "of his own age 28".
To sum up the conclusions one can draw from the Latin:
- William Brereton was painted in soldierly garb, explaining the sword
- The painting was created when William Brereton was 28