Yes and no.
Both "although" and "though" can mean what "but" means, even if both also have other definitions that don't quite mean what "but" means. That said, while that particular meaning may essentially be the same in substance, "although" and "though" are different than "but" in function, grammatically speaking.
"But" is a coordinating conjunction, but "although" and "though," whenever "though" is a conjunction rather than an adverb, are not coordinating conjunctions but are subordinating conjunctions.
English has only seven coordinating conjunctions (i.e., but, and, for, or, nor, yet, so). When coordinating conjunctions introduce a clause, the clause they introduce is a coordinate clause, which is a type of independent clause or main clause. In written grammar, a coordinating conjunction that introduces a coordinate clause to an existing sentence adds a second main clause and generally, with very few exceptions, must be preceded by a comma. What's more, because a coordinate clause is an type of main clause or independent clause, it can stand on is own as a sentence. That means you can start a sentence with "but" and have that be the only clause (e.g., You can properly say or write as a complete sentence: "But I don't want go.").
English has numerous subordinating conjunctions, which "although" and "though" are among. A subordinate clause is a type of dependent clause, not a main clause or independent clause. That means when "although" and "though" are used as conjunctions, they cannot stand independently as a sentence (e.g., You cannot properly say or write as a complete sentence: "Although I don't want to go."). Instead, as subordinating conjunctions, both "although" and "though" introduce clauses that are dependent on another main clause (e.g., "Although I don't want to go, I will.").
What can be confusing is, unlike "although," "though" is also an adverb, not just a conjunction. As an adverb, it modifies the verb or entire clause as being in someway thematically contradictory to what has been previously said, implied, or assumed, much like "but" does as a conjunction. As an adverb, though, unlike a conjunction, you can put it nearly anywhere in the sentence, not just at the beginning of the clause, like in this sentence, notice how "though" appears between commas after the word "adverb," but you wouldn't be able to aptly put "but" there in its place because "but" isn't an adverb. Likewise, because "although" is also not an adverb, only a subordinating conjunction, you wouldn't be able to put "although" there in its place, either. Your second example sentence is a good example:
- "I have a car. It is very old, though."
In that example of yours, "though" is obviously not a subordinating conjunction since it's not introducing the clause. How could it? It' comes after the clause. In that example, it's an adverb that modifies the preceding clause, a main clause. It must be written as two sentences because they are two clauses that aren't joined by a conjunction. Also, in as much as "though" essentially conveys the same idea as "but," its grammatical function is very different, which becomes obvious when you consider replacing it with "but," or even "although," i.e.,
"I have a car. It's very old, although."
"I have a car. It's very old, but."
Neither of those sentences above are grammatical or would be said by a native English speaker. That's because neither "but" nor "although" are adverbs, like "though" is in that sentence. So, even though the basic meaning of "though" is the same as "but," meaning the idea it conveys is the same, its function is completely different.
SHORT ANSWER:
Yes, "although" and "though" can mean what "but" means, along with meaning other things "but" doesn't mean, but "although" and "though" do not perform the same grammatical function "but" does, so while they share some definitions that are essential the same, their usage in English is different than that of "but" because of "but" being a coordinating conjunction and "although" and "though," as conjunctions, being subordinating conjunctions.
