В ванной вода плохо уходила, потому что в трубе был засор.

Because the subject is вода (water), which is grammatically feminine in Russian. In the past tense, verbs agree with the subject in gender and number:

• вода уходила = water (fem. sg.) was draining
  Compare:
• сток уходил (a drain, masc.)
• воды уходили (waters, plural)

Уходить can mean “to leave” for people, but it also has a common meaning “to drain / to run off” for liquids:

• Вода уходит = the water drains / goes down
  So вода плохо уходила is “the water wasn’t draining well.”

плохо is an adverb meaning “badly / poorly,” and with drainage it often implies “not properly,” which can include being slow, not going down fully, backing up, etc. If you want to be more specific, Russian can say:

• медленно уходила = drained slowly
• не уходила = didn’t drain (at all)
  But плохо уходила is a very natural all-purpose complaint.

Imperfective past (уходила) describes an ongoing state/background situation: the water “was draining badly” (over a period of time, as a situation you noticed). Perfective (ушла) would sound like a single completed event:

• Вода плохо ушла = the water drained poorly (that one time / it did drain, but badly)
  In complaints about a drain not working, imperfective is typically what you want.

В ванной means “in the bathroom” (location), setting the scene: “In the bathroom, …” It’s в + prepositional case because it answers “where?” (где?):

• в ванной (where?)
  If it were motion “into,” you’d use accusative:
• в ванную (where to?) = into the bathroom

Strictly speaking, в ванной most directly means “in the bathroom” (room) because ванная = bathroom. “In the bathtub” is usually:

• в ванне
  However, in everyday speech people sometimes say в ванной in contexts like this and mean “in the bath area / bathtub,” but if you want to be unambiguous, в ванне is the clearer choice for “in the tub.”

Because потому что introduces a subordinate clause of cause (“because …”). In Russian, the main clause and the потому что clause are normally separated by a comma:

• …, потому что …

Yes. You can front the reason clause, and the comma rules still apply:

• Потому что в трубе был засор, вода в ванной плохо уходила.
  Both versions are correct; the original simply starts with the setting (В ванной) and the symptom first.

в трубе uses в + prepositional again because it’s location (“in the pipe”), answering где? (“where?”). If you needed motion into the pipe (rare in this context), you’d use accusative:

• в трубу (into the pipe)

засор means a “clog / blockage” (usually in plumbing, but it can be used more broadly). Common patterns:

• засор в трубе = a clog in the pipe
• устранить засор = remove/clear a clog
• из-за засора = because of a clog (using из-за)

Russian often expresses this idea as “there was a clog”:

• в трубе был засор = there was a clog in the pipe
  You can also say “the pipe got clogged”:
• труба засорилась (perfective) = the pipe got clogged
• труба засорялась (imperfective) = the pipe would get clogged / was getting clogged
  The sentence you have is a neutral, very common “there was X” structure.

In the present tense, yes:

• В трубе засор. = There’s a clog in the pipe.
  But in the past you normally use был/была/было/были:
• В трубе был засор. = There was a clog.
  Omitting был in the past is possible in some styles, but it’s not the neutral everyday default.

Common stress patterns learners ask about:

• уходи́ла (stress on -и́-)
• засо́р (stress on -о́р)
• потому́ что (stress on -му́-)