So first of all I wanted to heat my 5* weapon at a 75% chance and it failed 3 times

Yep, that will happen sometimes. At other times you'll do many successful forgings and have nothing to complain about. I see no evidence here that the RNG is working incorrectly, but I can understand why you would be frustrated.

Second of all I've been hunting alchemy orbs for a long time now (past 3 days) and have yet to find a single orb. I've done 6 clockworks runs ran into 6 Treasure vaults, done 4 Vanaduke runs, nothing. And my friend who hasn't played the game in ages joins me for 1 second and gets 2 orbs in 5 mins.

Yes, that will happen sometimes. Your default expectation should not be to find orbs, but rather to buy them with energy. When you actually find the orbs you need in the Clockworks, you should be pleasantly surprised.

For what it's worth, the software is probably using a very standard RNG with well-established statistical properties. It is probably working extremely correctly. It's just a natural human response to get frustrated when the randomness doesn't go our way. Best wishes. :)

Hasn't anyone told you that you always go for the 3x Multiplier on the forge?

This seems to come up about once a month, and I always bite for some reason, but here I go again:

My advice is to use medium chances. On average, this strategy saves you about 7% of your Radiants, compared to the strategy of using 100% chances. However, in adopting this strategy you have to accept that sometimes you will get lucky and sometimes you will get unlucky. That is, you need to have a disciplined, long-term view of your Radiant use. If you have such a view, you end up saving Radiants, on average.

My guess is that the original poster will have trouble adopted this disciplined, long-term view. S/he should just use 100% chances, as Blazecat-Percival recommended.

Edit: Fixed typo.