All the things above are fully realizable in the coming decades, they are not in the realm of science fiction what so ever they are merely engineering problems.
2. Define “technology”
The meta-technology of R&D and socio-economic programs that will make these things happen exists and gets better every day. If a method to perform the needful does not exist, it will given the right conditions.
The only thing you need to do is to be patient. A lot depends on how greedy you are, if you want a smaller one it gets exponentially easier.
Just read this 10 year old report: https://space.nss.org/technologies-for-asteroid-capture-into...
"Reasonable" is subjective to define, but there are many multi-decade projects running right now so I don't think of multi-decade projects as unreasonable.
Things like sending man to the Moon or building Space Station would have been deemed "pure sci-fi" with the approach of the parent commenter.