Class-slaying

You realize brave Lyn's Sacae's Blessing cancels distant counter on swords, lances, and axes. Besides there are bajillion counters for them these days, especially Reinhardt. Reinhardt counters include any green mage with good magic bulk (Julia, Deirdre, Sonya, even Nino to a degree), green dragons, green armors (even low res ones can survive with high enough hp) and daddy Sigurd can't be killed by him at full health. Brave Lyn counters include dragons with Lightning Breath/DC (with the refine effect of course), raventomes, and she can be killed by any physical brave weapon due to her paper thin defense.

Fjorm with the original weapon and kit can handle Reinhardt.
You don't need to change her.

No and no.

My suggestion is invest in a green mage with the raven build and bowbreaker

literally just build a Green Gronnraven+ user,,,,,,,

If you’re really considering giving Fjorm a ridersbane with DC, I’d say reconsider your team. You should have a unit that can handle Brave Lyn, and another capable of taking down Reinhardt. Fjorm with the right build kills Reinhardt (unless he runs lancebreaker, which makes it impossible to kill him on enemy phase and makes it likely for Fjorm to die), but you should be running a green unit that can kill Reinhardt (usually in one hit) and a unit strong enough to oneshot Brave Lyn or capable of doubling her.

If your goal is to stay in tier 20 arena, start investing in armoured units. You'll eventually stop facing horse emblem teams once your team score gets high enough. Since I'm assuming you're F2P, units like Draug, Sheena, Gwendolyn, and Effie are pretty darn good units. Running DC and wary fighter with horse slaying weapons should allow you to tank and then one shot them. Fjorm with DC and ridersbane won't have much use once your arena scores get higher, but a well built armoured unit will still be very viable.

Bowbreaker should do the trick, give that to a unit with QR as a S slot.

I just use Micaiah with deathblow, I can't bait them but she one shots them, but I'll assume you don't have Micaiah, a good option is a green gronraven+/triangle adept3/bow breaker user, I have a 5* +4 Cecilia and Inigo +2, Boey works too.

My solution against b.Lyn and reintardt. Yes I know b.Lyn special blessing prevents counter, but unless she gets repo away, I kill her on my turn.

I haven’t seen anyone else mention this (apologies if anyone did) but why not give zanbato to Olivia and refine it for whatever it is you need? I know you need Gray for this so if you don’t have him I understand, but I don’t see the need to take a DC weapon off a unit just to give them DC as a skill. Alternatively, give Fae bowbreaker 3 for a 4* Setsuna?

I use a DD3, Bowbreaker3, Gronnraven+ (or Keen Gronnwolf) (F)Robin for those two. She does a damn good job keeping them in check. I struggle a lot more with the Swift Sparrow B!Lyn than I do with Rein, so that’s why BBreaker.

With Sacae’s Blessing, B!Lyn will still wipe the floor with Fjorm, don’t bother foddering the best unit in the game to give her DC. :)

If you're not up for a gronnraven tome user, a fast green tome with a defense of about 20 or higher will work. He wasn't built out for this, but I bait out most B!Lyn's with Soren (19def + 6hone +3spur + 4 for adjacent support unit w/refinement = 32def; if not running a tactic team, I give him DD3). 41spd (without buffs) means he won't be doubled even with swift sparrow, and he can easily take a single hit from her and OHKO her (especially if she got chilled). (Reinhardt is no threat. I haven't found a single Rein who can take out Soren) No raven tome required!

If it's a brave bow Lyn, VL!Ike baits her out instead; Firesweep is the only really tricky one (but it's rare); Most of the time I can still bait her with VL!Ike and charge aether to kill her next round.

Instead of looking for one unit who can counter both all the time, why not try to think of ways each of your units can counter the common builds?