Private proxies or thousands of public ones if you must.
What about filters? Settings? Types of links? Types of engines? How many keywords in the keyword field? What about the spec of your machine? Internet connection?
Lots of more reasons LPM could be low than just the information you've given.
From those screenshots you're not using proxies for anything. You need to tick the box next to each section you want using proxies, and then tick what type of proxies you want to use there.
I'd also change 'If a form field can't be filled' to Choose Random, and select more search engines to use
Yes. If you want to use proxies, make sure 'Use proxies' is checked, and check the box next to 'Search Engines', 'Submission', and whatever else you want to use them for. Then, click either public or private. Using public proxies will usually mean horrible results, unless you have an extremely high-quality filtered list.
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I'd also change 'If a form field can't be filled' to Choose Random, and select more search engines to use