I added a new page to the Hook Up Spanish Phrase Guide about asking and responding about who you live with. Examples:

Do you live by yourself?
¿Vives solo/a?
¿vee-vehs soh-loh/ah?

Who do you live with?
¿Con quién vives?
¿kohn kee-EHn vee-vehs?

I live alone.
Vivo solo/a.
vee-voh soh-loh/ah.

I have a room mate.
Comparto piso.
kohm-pahr-toh pee-soh.

More Spanish phrases discussing who you live with over here.

I added phrases about finding out if someone is available or in a relationship to the Getting background info section of the Hook Up Spanish Phrase Guide.

Here's some phrases I added:

More here.

When you become interested in someone, one of the first things you
typically want to find out is whether they are currently dating someone.  If they are, then that might be enough to make you move on to the next person.  However, you might also find out how serious they are in their current relationship (whether they are dating someone casually or exclusively).

There's a number of ways to describe a relationship from casual
to serious:

They're just fooling around.
Sólo están vacilando.
SOH-loh ehs-tAHn vah-see-lahn-doh.

They're friends with benefits.
Son amigos con derechos.
sohn ah-mee-gohs kohn deh-reh-chohs.

They are boyfriend/girlfriend.
Son novios.
sohn NOH-vee-ohs.

They're serious.
Andan de novios.
ahn-dahn deh noh-vee-ohs.

They are engaged.
Están prometidos.
Eh-STAHN proh-meh-TEE-dohs.

Of course, one of the best ways to find out whether or not someone
is available is to ask:

Do you have a boyfriend/girlfriend?
¿Tienes novio/a?
¿tee-ehn-ehs noh-vee-oh/ah?

In some countries a boyfriend is called novio (NOH-vee-yoh)
whereas in others novio means more of a fiancée and a boyfriend is
called amigo (ah-MEE-goh).  You might need to clarify this when
talking with someone.  If they say tengo novio (TEHN-goh
NOH-vee-yoh), you can ask if they are engaged (see above) or just
dating. 

Similarly, if a man says Ella es mi amiga (EH-yah ehs mee
ah-MEE-gah), you might need to clarify if they mean girlfriend or
just friend.  Not only do you want to know this before you ask
someone out, you need to be aware of this when referring to your
own significant other and friends so that you don't convey too much
or too little commitment in your own relationships.
 

When it comes to dating knowing whether or not a person is available is one of the most important things on the checklist.

If you want to ask if someone is single you would use the word soltero for a male and soltera for a female:

Are you single?
¿Eres soltero/a?
¿EH-rehs sohl-TEH-roh/ah?

When asking if someone is single, you use a conjugation of ser or estar as the verb. Depending on the area where you are, you might find one used more than the other, but they are generally interchangeable in this context.

He/She is single.
Está soltero/a. (estar)
eh-STAH sohl-TEH-roh/ah.

He/She is single.
Es soltero/a. (ser)
ehs sohl-TEH-roh/ah.

Solterón (sohl-teh-ROHN) for males and solterona (sohl-teh-ROHN-ah) for females are a stronger way to say soltero/a but their meanings are quite different.

If a male is said to be a solterón this could mean that they are either a confirmed or long term bachelor. This isn't to say that they might never want to settle down, but chances are they are more of a player than someone interested in commitment.

On the other hand solterona tends to categorize a female being an "old maid" which is much more derogatory than the male version, so you wouldn't want to ask someone ¿Eres solterona? or you might be wearing a drink instead of sharing one.
 

The literal translation of the above phrases is "Are you accompanied?"

Here's a couple ways to ask if someone is traveling alone or with others:

A couple responses to any of the above:

I’m by myself.
Estoy solo/a. (o= for males, a= for females)
ehs-toy soh-loh/ah.