Grammar – How Should Verb Go with ‘Let’ in Past Tenses?

The two sentences violate the sequence of tenses. They should be:

"He has agreed to help me, so I will not do my homework."
"She has suddenly decided to go back, so I have decided to go alone."

First comes the action in the first clause in both sentences, then the decision in the second clause in both sentences. You cannot go from the present prefect to the simple past that way. The sequence is past perfect to simple past or simple past to simple past:

"He had agreed to help me, so I did not do my homework.
"She had suddenly decided to go back, so I decided to go alone."

Another way of writing these two sentences is:

"Because he has agreed to help me, I will not do my homework."
"Because she suddenly decided to go back, I have decided to go alone."

In both cases, there's a cause-effect relationship stated.

Here's another link

EDF had expected to build the £18bn plant

In this case, "expected" is the past participle (on regular verbs, past participles are identical in form to the past tense) of the verb expect, so the past perfect with the had is still there!