Mounting a block

Make it a mob but uncheck the AI box and make it mountable

I would like this too. And to actually make it a block instead of an entity. That would be very helpful for modding.

In vanilla minecraft i spawn an invisible and invincible horse with commands XD

But how do I use an item to spawn it where the player is looking? It would be weird to have a chair spawn egg...

Try something like this (this allows you to still use a block and model for the furniture):

Use the "on block placed" event trigger inside your block's triggers page. Inside that procedure, use the world management category to add the "run command at (x y z)" block. Use the command to summon an invisible pig with a saddle and no AI at the same coordinates as the furniture block (but tweaking the y value to get the player's seating correct). 

/summon minecraft:pig ~ ~1 ~ {NoAI:1b,PersistenceRequired:1b,Silent:1,Invulnerable:1,Saddle:1,Age:0,ActiveEffects:[{Id:14,Amplifier:0,Duration:2147483647,ShowParticles:0}]}

you could also instead of a pig make an entity that was the same size of a block or smaller and rideable so that the hitbox would be the same size.