Hi!
1. I recommend chapter 1 & 2 of this documentation for performance tuning.
Their site use a subscription based search service (algolia, and not a wordpress site either), which charges monthly fees to run a search service on an external server – which is very fast – but costly. This plugin however runs on your local server, but there are no subscription or any monthly fees – the performance will depend on the host server performance.
2. That look I’m afraid is not possible with this plugin. You can however change the floating results width here.