Suggest : How to Fix this Redirection Issue
I have 500-1000 urls in a domain and would like to redirect all the links to another domain(new).

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Please suggest how would be the impact to the new domain after bulk redirection.

You can suggest other best ways to redirect all 1000 links to new domain.

Also suggest, whether I should redirect all links to a single page or redirect all individual links to their respective new domain links.

Awaiting for your suggestions.
The best way is url-to-url redirect.
Usually our dev creates the special sheet (via Google docs for example) this columns 'old url'->'new url'. We migrate large ecommerce site in this way.
evacuate Web Browser Redirect Virus, pursue these means: 

Stage 1: Print out guidelines before we start. 

Stage 2: Use [removed] to end suspicious projects. 

Stage 3: Use [removed] to Scan for Malware and Unwanted Programs 

Stage 4: Scan and clean your PC with [removed] Anti-Malware 

Stage 5: Scan and clean your PC with [removed] AntiMalware. 

Stage 6: Use [removed] to expel adware from a PC. 

Stage 7: Reset programs back to default settings. 

Stage 8: Run [removed] to discover obsolete and defenseless programs.
evacuate Web Browser Redirect Virus, pursue these means: 

Stage 1: Print out guidelines before we start. 

Stage 2: Use [removed] to end suspicious projects. 

Stage 3: Use [removed] to Scan for Malware and Unwanted Programs 

Stage 4: Scan and clean your PC with [removed] Anti-Malware 

Stage 5: Scan and clean your PC with [removed] AntiMalware. 

Stage 6: Use [removed] to expel adware from a PC. 

Stage 7: Reset programs back to default settings. 

Stage 8: Run [removed] to discover obsolete and defenseless programs.
What are you going on about? There's no mention of virus, or redirect virus issues. Can you advise what your post has to do with the OP's quandary?
I have 500-1000 urls in a domain and would like to redirect all the links to another domain(new).

Please suggest how would be the impact to the new domain after bulk redirection.

You can suggest other best ways to redirect all 1000 links to new domain.

Also suggest, whether I should redirect all links to a single page or redirect all individual links to their respective new domain links.

Awaiting for your suggestions.
As far as I know, you can expect to lose some ranking, at least initially. 301 redirections don't pass on all of the original link juice, so you should see some loss in traffic after the move.

I don't know how to suggest you a better way of redirecting since I don't know your current method.

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If you keep your site structure the same and only change the main domain, definitely redirect all the pages to their new counterparts.

I would also suggest an additional step: After you have made the move, get in touch with the people linking to your old domain and ask them to change the link to the new address. This should alleviate some of the ranking loss over time.

Hope this helps!
301 redirect pass 100% PageRank, but it depends on some factors (content, page designe/structure). If you just migrate from url1 to url2, you won't lose any position. From my experience (for example migration from Magento 1 platform to Magento 2 platform, that means significant changes) positions have recovered in 1-2 weeks