Since I had not known killed horses were able to respawn, I had bought another, and now I need to store both, what to do?
In vanilla Skyrim there isn't a place to stable your horse.
The horses you own do tend to stay wherever you leave them - albeit vulnerable to hostile forces and their whimsical AI - and stables in Skyrim tend to be among the safest places to leave your horse.
The most recent horse you've ridden will be your active horse, and will reappear wherever you fast travel - that is, unless you travelled to one of the major towns (since your horse can't follow you inside). Then you can find your horse at the stables of that particular town.
As per elderscrolls.fandom.com:
Once purchased, a horse is considered owned and can be identified by the "Player's horse" label on the HUD. One can own multiple types of horses and multiple horses of the same type. The horse last ridden or fast traveled with is the one that accompanies the Dragonborn [the active horse]. Any other owned horses return to the stable where they were purchased.
When dismounted, owned horses will stay in the spot you left them, but stolen horses will run home.
As anything that is vaguely flawed in Skyrim has already been modded, you might might want to give the Horse Stabling mod a chance to mend this 'defaulty' behaviour.
Horse Stabling is activated by riding your horse to the area in front of the stable, dismount then walk away. At cities the hostler will come and walk your horse into the stables and at your Hearthfire homes your steward will take care of it. If you don't have a steward or the hostler is not there the horse will walk into the stables on their own. When you are ready to leave just get on and ride off.
You don't own the dead horse anymore, you have to rebuy it. You can't store a horse, the last horse you rode will fast travel with you.
All of the horse information is available on this page and can answer any further questions about how horses work.