(d) Can you remember me to go to the bank?
Can you remind me to go to the bank? ‘Remember’ refers to the past and ‘remind’ refers to the future. For example you can remember an event that occurred in the past but you can only remind yourself or others of an event that needs to occur/or will occur in the future.
It can also operate in the present e.g. "May I remind you this is a court of law."
I am absolutely agree with you
I absolutely agree with you. (I am really stuck on this one)
The sentence is half-way between Present Continuous - "I am absolutely agreeing with you", which is colloquial for "I am agreeing with you absolutely" and Present tense, as you have given. Since the phrasing of the first sentence is more colloquial (I'm absolutely agreeing') and this is a formal test of English, it would be better to choose the sentence that you did!
It’s not sure it’ll rain today
I am not sure if it’ll rain today. ‘It’ does not refer to a person so it does not make sense to ‘it’ in this sentence. ‘I’ would be the better pronoun to use. ‘am’ is the verb that is used after ‘I’. Because the subject (I) is not sure if it will rain (it may or may not rain) and ‘if’ introduces a condition that may or may not happen, then ‘if’ is placed before the main clause.
Better to say, the sentence requires a personal pronoun in the nominative, rather than singling out "I".
Whether 'if' is required is 'iffy'. In the sentence, "He's not sure it'll rain today", it may be wished that it will rain because someone has scattered lawn fertilizer/weed/moss killer, which requires a thorough soaking within 2 days. Hence, if someone is expressing pessimism, the complete sentence might be, "He's not sure that it'll/it will rain today. (You might have to use a sprinkler instead.)
(j) I’m boring with this exercise
I’m bored with this exercise. This is a passive sentence and the past participle bor(ed) is used after the irregular verb ‘am’.
This isn't to do with voice. If you are asked to 'spot the mistake', then I can think of a context in which the sentence as given could be appropriate (hence no mistake!...but the context would not be common).
Then, the two possibilities are that (i) 'you' has been omitted; "I am boring you with this exercise", said by a frustrated instructor, or (ii) as you have suggested, "I'm bored with this exercise." The frequency of usage of the respective sentences suggests that your option, (ii), is the better.
(However, since it is open for you to state your reasons, you could thus state ALL your reasoning and logical deduction, and be particularly impressive!)
THE REST ARE FINE!