Firesweep Lance+ inheritance.

Yes. Cordelia's best builds use it. With the Guidance seal on her she's on just about any team I use.

If she's +spd, yes. If she's +atk, she works Brave Lance better.

If you have Tana then put it on her

Depends on her IVs and what you want out of her. I personally have a +SPD-HP Cordelia with a quad build and summoner support. With a single merge and a life and death kit on her, she hits 50 attack and 41 speed before any flier buffs. I run a quad goad team since I have 3 Brave weapon users in my flier team (her, Elincia, and Cherche) along with a supertank in Michalis, which pushes her stars to 62/53. Even without support and the merge a quad goad takes her to 60/50, more than enough to quad everything she fights and kill just about everything in sight.