Breakdown of Пускай велосипед ржавый, но он всё же мой любимый.
он
he / it (for a masculine noun) / it (for a neuter noun)
мой
my / mine
велосипед
bicycle
но
but
Questions & Answers about Пускай велосипед ржавый, но он всё же мой любимый.
Is there any difference between using пускай instead of пусть here?
In this sentence, they mean exactly the same thing ("even if" or "granted that"). Пускай is just a slightly more conversational or colloquial version of пусть. Both perfectly set up this kind of "even if X, still Y" contrast.
Why are both но and всё же used together in the second clause?
When you start a sentence with пусть or пускай, the second half needs to resolve that setup with a contrast. You could use just но (but) or just всё же (nevertheless/still). Using them together as но он всё же ("but it is still") is extremely common and strongly emphasizes the contrast.
Could I use даже если (even if) instead of пускай in this sentence?
You could, but the tone shifts slightly. Даже если usually introduces a hypothetical condition (the bike might or might not be rusty). Пускай, on the other hand, concedes a known fact: you are admitting the bike is rusty right now, but stating it doesn't change how you feel about it.
Why does любимый stand alone without a noun at the end?
Russian frequently lets adjectives stand alone when the noun is obvious from the context. Since велосипед was just mentioned, мой любимый simply means "my favorite [one]".