How do I only dp or do just the lines, not the entire block in Vim diff?

There are a number of ways to do this.

1. Select the range of lines in the destination buffer that you want to obtain from the source buffer and use :diffget. For example, you could visually-select a range of lines with V, then type :diffget.
2. Select the range of lines in the source buffer that you want to put into the destination buffer and use :diffput. For example, to put the current line into the other buffer, type :.diffput.
3. Use yank and put. Select the range of lines in the source buffer that you want to copy into the destination buffer, yank them using Y, move the cursor to the destination buffer and put them where you want them with p or P, then delete the lines you don't want.
4. Yank as above, but in the destination buffer, visually-select the range of lines you want to replace (not necessarily the same number of lines) and type "0p. That uses the 0 (zero) register which always contains the text of the most recent yank.

To "refresh" the display to show the proper highlighting, execute :diffupdate or simply :diffu. Sometimes that isn't sufficient and you need to move the cursor to the other window to complete the refreshing.

You can read more about copying diffs in

:help copy-diffs

I also wanted to modify one line at a given moment during a diff. So I created a simple map and put them in my vimrc file.

nnoremap <silent> <leader>dp V:diffput<cr>
nnoremap <silent> <leader>dg V:diffget<cr>

You could use do instead of dg, but I am more used to thinking "diffget" instead of [o]btain.

For your bonus, I just use a another simple map twice:

nnoremap <silent> <leader>df :call DiffToggle()<CR>

Now, df will turn off/on the diffmode, so I just turn it off and back on.

And a bonus option is to add

nmap <silent> <leader>du :wincmd w<cr>:normal u<cr>:wincmd w<cr>

This will allow you to undo a typo or unwanted change on the other file/window, because :undo of just u will only undo a change in the present window.