AE86 4age engine not starts crank ok backfires to air intake

[Bean]

I think you're on point with assuming several issues.

Jondee may very well be correct on the cold start part. I guess the valve underneath the throttle body (with the wax element) is stuck in closed position. This would at least make sense why you have to push the accelerator while cold but not once the engine is warm. This will also result in too mich fuel being injected or more accurately not enough air to burn the fuel injected.

Very dark oil after such a short period does point to a failed seal (headgasket or valve stem seals). This is a long shot but technically if you the stem seal failed sufficently exhaust and fuel may be pushed into the head and from there to the intake plenum.

If you can get hold of a leak tester (similar to a compression tester) you should get some more results (mind you a failed stem seal won't show there but exclude other points).

Best of luck.

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