Is there any key combination that simulate the Del in Vim insert mode? For the Backspace, there is the Ctrl-H which is very convenient, and make it easier than pushing the far away Backspace button.
You can map keys yourself in vim, including insert mode. The following article reveals more details: Mapping keys in VIM
Take a look at http://vimdoc.sourceforge.net/htmldoc/insert.html There are a few more built-in key combinations for various tasks.
Also you can set your own mappings using .vimrc for example your given example is just
imap ^H <Left><Del>
On my vim installation, Del in insert mode Just Works. :help i_<Del>
If Del isn't doing what you want, you can try :fixdel
. :help :fixdel
has a good explanation of what that tries to fix.
If you simply wanted to simulate Del via another Ctrl-key mapping (e.g. Ctrl-D), I'd recommend the following mapping:
imap <C-D> <C-O>x
Ctrl-O in insert mode will allow you to run a single normal mode command and automatically return back to insert mode. x
deletes the key under the cursor.