I would say #1 or #2 is fine:
I forget how to do algebra: Puts the act of forgetting in the present. Maybe you do generally know it, but you can't remember right now, so you can't help.
I've forgotten how to do algebra: that is, sometime between when you learned algebra and now, you've forgotten how to do it. The act of forgetting is somewhere in the past ...
They all are correct, but the meaning is a bit different.
"I forget how to do algebra" means that there's some regularity to that; that you need to do some algebra from time to time, and every time you can't remember how to do it.
"I've forgotten how to do algebra" means that you have forgotten it some time ago. For example, you last did ...
Yes these are the simple past and two forms of the present perfect. There are two forms because there are two possible past participles: "gotten" (Common in American English, less common in British) and "got" (British English uses this almost exclusively, American English uses both "got" and "gotten", there is ...
This is "future in the past"
The story is being told in the past tense. It is a past tense narrative. Then there is an event that is in the future of that past time. For this we use "would" instead of "will".
Compare a present tense narrative
John has a guitar. He practices every day. He will be a famous pop star when he ...
This is "future in the past".
Historically, various modals were originally in pairs, present and past:
will - would
can - could
may - might
shall - should
All the historically past forms have their own separate meanings now, but they are also used as past tense forms in some contexts.
The most common context is reported speech:
He said "I ...
One cannot use "later today" to mean "at a later time today that is already in the past. If the meaning is "I gave it to him at a later time today" something like the following might be said:
A: When did you give John the document?
B: Today, but not this morning. I gave it to him later in the day, perhaps around 2 pm.
A2 is simple past tense, and so is incorrect. A1 is a correct option, using the present perfect tense to talk about a point in the future. Other correct options would include:
"... if you finish your work by then" (present tense used for a type 1 conditional
"... if you will have finished your work by then" (future perfect tense)
"He dreaded to think what might happen next."
Dreaded is the only word that can be changed to its past tense form. Since changing either think and happen to its past tense form makes this,
"He dread to thought what might happen next."
"He dread to think what might happened next."
As you can see, both ...
Both are correct.
Americans are more likely to use the simple past "tried", and native speakers from other countries are more likely to use the present perfect "has tried". There's no functional difference.