Conditional origin is already answered here: What is the historical origin of the French présent conditionnel?

Imperfect is a direct evolution of the same tense in Latin, with the noticeable fact an ‘s’ has been added to the first person singular.

amabam   → amava   → ameie   → aimoie  → aimois   → aimais
amabas   → amavas  → ameies  → aimoies → aimois   → aimais
amabat   → amavat  → ameiet  → aimoiet → aimoit   → aimait
amabamus →           amiiens →                      aimions
amabatis →           amiiez  →                      aimiez
amabant  →           ameient →           aimoient → aimaient

Reference: http://monsu.desiderio.free.fr/curiosites/imparfait.html

The simple future has been designed a similar manner than the conditional, from periphrasis:

amare habeo   → amareo   → aimerai
amare habeas  → amareas  → aimeras
amare habet   → amarea   → aimera
amare habemus → amaremus → aimerons
amare habetis → amareis  → aimerez
amare habent  → amarent  → aimeront

As you see, its no surprise if you recognize the avoir verb in the future tense endings as that very verb was already used in Latin.

Reference: http://monsu.desiderio.free.fr/curiosites/futur.html