This is my first build, and I've run into a couple problems,

I am building my road bike from a 1981 Fuji Sports-12 frame. I upgraded from the original crankset to a Shimano SORA R3000, but when I re-assembled the bike, the chain has tons of slack when its on both of the smallest rings. It didn't have this problem on the old crankset, so I'm wondering if the smaller front ring on the new set is just smaller in diameter, causing more slack? The Rear wheel is actually set further back in the dropouts now, so I don't think that is the issue. I want to be sure this is the issue before I take out some of the chain links.

I'm also having an issue with the friction shifters... They shift just fine when I turn them, but are immediately pulled back to their original position and the bike shifts back. Should I be setting the cables when the shifters are already pulled all the way down?

I appreciate any help. Thank you

There are smarter people than me here who will do better, but if you are using the same rear derailleur, if you have a smaller small ring, it would account for the slackness.

if you search online for “sizing a chain”, you can get rid of the slack by removing a few links.

sheldon Browns website is enormously helpful about all things bicycle.

PS
1. tighten cables when they are in the small sprocket position (parallel to the down tube). Any slack is likely to be pulled by the derailleur springs
2. You might want to list the components and let the resident gurus check compatibility with crankset, chain line and shifting. Friction will shift anything but chainline is important.