I disagree about Rolf. Rolf is an excellent unit. He ends up slightly better than Shinon, but you do have to train him. Gatrie is a much better choice than Brom, because while they both have a 60% defense rate, Gatrie also has a 60% speed rate and a 35% res rate, both much higher than Brom's own rates.
Honestly, Mist is far inferior to Elincia. While they have similar defense and resistance rates, Elincia's strength is 40% higher than Mist's and her speed is 20% higher. Elincia's weapon is very strong, gives a brave effect, and doesn't break, while Mist's weapon doesn't even work as intended, so Elincia will be the better combat unit. Elincia's magic rate is 80%, while Mist's is 40%, so Elincia will be better at healing as well. Elincia also rides a pegasus, which grants obvious benefits to just a horse. Use Mist for healing in Ike's, but you shouldn't take her to the endgame.
Consider dropping Brom for Gatrie and Mist for Elincia based on stats, which would free up space in Ike's chapters for Oscar.
Also, you have to use the silver card immediately, because it disappears after you leave the base.