If I give an Ochran Assassin trample and attack with it, does it destroy all of the opposing creatures, which are forced to block it?
No, trample has no effect on how an attacking creature deals damage to defending creatures.
With or without trample, an attacking Ochran Assassin can destroy any number of blocking creatures, up to its power. So if the Assassin has 3 power, it can destroy up to 3 creatures. This is because Deathtouch only has an effect if at least 1 damage is dealt, and any amount of damage with Deathtouch is lethal. So the Assassin can assign its total damage as power, split into one per blocking creature, and each creature it deals damage to that way is destroyed.
The only effect trample has is to allow you to assign excess damage that is not needed to destroy any creatures to the defending player. For example, if the Assassin has 5 power and the defending player only controls 3 creatures that can block, the Assassin can damage and kill all 3 creatures and also deal 2 damage to the defending player. But if the Assassin only has 1 power, it can still only destroy 1 creature.
Not necessarily all of them.You have to assign lethal damage to each blocking creature, and deathtouch here means that lethal damage is 1; therefore you can kill as many creatures as your Assassin has power - and unless you've increased its power, that's still only going to be one creature. Trample doesn't make a difference to the number of creatures destroyed, only to whether any excess damage goes through to the player or planeswalker you're attacking.
Any amount of damage greater than 1 is excess damage if the source dealing that damage to a creature has deathtouch
Trample will play no part in how many creatures get destroyed by a creature with deathtouch. How Deathtouch works is defined in the the rules as rule 702.2. The important parts for this question are parts 2b and 2c:
702.2b A creature with toughness greater than 0 that’s been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action. See rule 704.
702.2c Any nonzero amount of combat damage assigned to a creature by a source with deathtouch is considered to be lethal damage for the purposes of determining if a proposed combat damage assignment is valid, regardless of that creature’s toughness. See rules 510.1c–d.
This works combined with the rules on assigning damage in the combat damage step (emphasis mine):
510.1c A blocked creature assigns its combat damage to the creatures blocking it. If no creatures are currently blocking it (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If exactly one creature is blocking it, it assigns all its combat damage to that creature. If two or more creatures are blocking it, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocked creature to divide its combat damage. However, it can’t assign combat damage to a creature that’s blocking it unless, when combat damage assignments are complete, each creature that precedes that blocking creature in its order is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it.
So the way this works is each creature blocking needs to be assigned lethal damage before you can assign damage to the next blocking creature. Normally lethal damage is damage equal to or greater than a creatures current toughness, however because of rule 702.2c this is changed to anything greater than 0, meaning 1 point is enough to be considered lethal and destroy the blocking creature.
Ochran Assassin is a 1/1 creature, unless that's been modified by other effects it only has one point of damage to assign and deal to blocking creatures. You as the attacker will get to choose which order it deals damage to, but with only 1 power it can deal "nonzero damage" to only one of those blockers, the rest will take no damage and not die. Damage naturally moves on to the next blocker when it finishes doing lethal damage to the previous blocker, Trample only affects what happens when it's on the last remaining blocker, either all remaining damage must be assigned to that last blocker(no trample), or any damage remaining after lethal damage is assigned to the blocker can be assigned to the defending player or planeswalker(trample).
A damage multiplier like Furnace of Rath or Dictate of the Twin Gods affects damage after it is assigned. A 1/1 Ochran Assassin will still assign it's 1 point of damage to only one creature and that damage will be multiplied when it's being dealt.
If you want your Assassin to kill everything, there are cards that will make it work, like Beastmaster's Magemark or Barreling Attack. You can also get a similar result by using Engulfing Slagwurm with something like Lure or Nemesis Mask.