If you go ahead and make a third table, you can then turn your website fields into linked fields and link them to the third table.

That should do what you want, though I'm unsure about free plan limitations in this area.

Is there any way to move records from table A to table B with one click?

Currently I have to select all records and then Ctrl+C + Ctrl V to new table. Instead can I just group and filter records and then move in single click?

If you turn your website fields into linked fields, that should auto-populate your third table with data without you having to move anything manually.

Here's an example base: https://airtable.com/shrM1Q8ApOCxWyzDL

If you want to see additional info from tables 1 and 2 within table 3, you'll need to use lookup fields.