Learn English – How should I make a (double-)negative sentence using “could have + past participle”

1. Who sent those flowers?- I'm not sure. It could have been your mother.

The above is correct written form. There's a lot of latitude with speaking, of course. Here are some alternatives:

• Who sent these flowers? Couda' been your mother.
• Who sent these flowers? Maybe your mother?
• Who sent these flowers? Could be your mother. <- not likely but understandable. This and other types of "incorrect and slightly odd" spoken responses happens often enough. It can make one think a second longer to fill in the gap or an opportunity to make a joke: "Oh! My mother turned into flowers? So who do you think sent my mother? (haha)"

2) He could have been Prime Minister now if he hadn't decided to leave politics.

The above is correct written form. You could find a place for your "could be" form in spoken language as a parallel, emphatic, emotional voice. The following illustrates this with a similar construction, but with some necessary context:

• Man #1: "It's not so bad...I'm doing well now... I've worked my way up to vice president of the Acme Corp!"
• Man's Tough Friend: "Don't give me that! You could be CEO now if you hadn't messed everything up in the first place."

3) We could have spent today at the beach, but we thought it was going to rain, so we decided not to.

The above third case is not correctly worded as you stated above. It doesn't make sense to say "I could have done X, but since Y I decided not to." That's because the decision was totally volitional. The format is "I would have done X, but since Y I decided not to." So the original sentence above would be more natural as:

• "We [were going to spend | would have spent] [the day | today] at the beach, but we thought it was going to rain, so we decided not to."

To use your original sentence wording ("could have spent"), it would need to be something less within the speaker's control, and perhaps an expression of disappointment like this:

• I could have spent the day at the beach, but Wendy got sick so I had to stay and babysit. Hrmph! (Note that this is also volitional in an absolute sense; yet has a sense of blame.)

To make it your alternative "could be spending" suggests a greater disappointment that is still ongoing and not fully accepted:

• On the phone: "I could be spending the day at the beach, right now, with all my friends, but Wendy just had to get sick and so I'm just stuck here baby sitting. Hrmph! (Note that this is also volitional in an absolute sense; but has a greater sense of disappointment and blame.)

The most mature way to handle the situation would be decisive and volitional:

• "Yes, I know... I was planning on spending the day at the beach with you guys. But Wendy got sick so I'm staying home to take care of her today. I'm certainly not going out if Wendy needs me. Have fun... I gotta go now. Bye."

1) Right. You don't know whether the plane was on time or some other factor intervened, but you fully expected him to arrive in Jakata this morning and have no reason to think he didn't.

2) Also right (mostly). "The week" is the present week, and "the end of the week" is yet to come (unless right now happens to be 5:00 pm on Friday, or midnight on Saturday, or whatever other time has been defined as the end of the week).

In 2) & 2a), "by" means "at or before," so the builders are expected to be done sometime between now and the end of the week.

In 2), the past perfect implies prior completion, so it means you expect the builders to have finished the work, swept up the debris, and left the site well before 5:00 pm on Friday (which I'm going to define as the end of the week for the purposes of this answer).

2a) is the simplest construction here, and the present simply means that you expect the builders to finish the work at or before 5:00 pm on Friday.

In 2b), "at" means "at (that moment)" so it would most strictly mean that you expect the last nail to be driven home at exactly 5:00pm on Friday. But, depending on context, "at" usually carries some leeway to either side of the time specified (perhaps especially so in the context of builders).

2c) is the only one that doesn't quite work. The prior completion of the past perfect and the immediacy of "at" are at odds with each other. It's not very wrong, but does sound off and it's not something I would say unless by accident.

(My landlord's got builders working at my apartment right now. They're not supposed to have finished until the end of week after next (that is, about two-and-a-half weeks from now), and there's a good chance they won't be done even by then.)