Yes to the first question. No to the second one.
This is currently located at the top of the Temple Mount.
It's illegal for Jews to ascend here without a police escort and no prayers may be said by Jews in this place. Jews have been incarcerated for making a blessing on the water they wanted to drink in the heat. An entire Temple is therefore obviously out of the question.
Also, there is apparently a way to at least vaguely determine the descendants of Aaron:
Y-chromosomal Aaron - Wikipedia
These markers only help determine that many people believing themselves to be priests descend from a single father. They don't say that that father was Aaron.
Also, God can make exceptions to allow non-descendants of Aaron to contribute to performing sacrifices if they are sanctified in cases when the situation simply does not allow for viable alternatives. Example: 2 Chronicles 29:34
It depends on the aspect of the service. If you look at Lev. 1:1-8 you'll notice the placement of the words indicates this:
v2 - speak to the children of Israel...
a man when he sacrifices a sacrifice to G-d...
v5 and
he shall slaughter the bull before G-d and the
children of Aaron the priests
they shall bring close the blood and they shall throw its blood on the altar...
v6 and
he shall skin the burnt offering and
cut it to its pieces
v7 and the
sons of Aaron the priest
they shall give it to the fire on the altar
I've highlighted for you the difference in wording. I've added in some extra "they's" because translations to English don't always indicate when a Hebrew verb is written in the plural form.
When the verse speaks in singular, it refers to the man who is bringing the sacrifice. When it speaks in plural it refers to the priests. So a non-priest may slaughter, skin and cut up a sacrifice. Only priests may take the blood from the animal, bring it to the altar, sprinkle it there and offer up the animal parts.