gene expression - What is the best way to express two proteins in a mammalian cell?

You can use a bidirectional promoter. The problem that you mentioned about proteins not expressed in same level happens because of competition for polymerase. But there are well optimized parts and also commercially available vectors that work fine.

You can clone genes in a serial order. It won't be a problem. Just leave a 100bp linker after the polyA signal of previous gene. If your cassette becomes too huge, then insertion becomes slightly difficult. That's why people use IRES or TA-peptides, etc.

Retroviral based insertions work quite decently, but you can't control copy number variation between different cells.

You can use two different promoters. The dynamics will depend on the promoter strength and concentration of inducer.