Hi there,
I can suggest you a good ajax search plugin and then will install and config it for posts and custom posts both. Everything you have mentioned will be there. Just created a site and it has the ajax search functionality same as you are looking for. Can show you live example.
Please feel free to discuss anything regarding this project before starting.
About Me:
My self Ajay KC, I'm a FULL-TIME Freelancer Designer Developer. I'm designing and developing Websites/Blogs for the past 7-8 years. I have good knowledge & and extensive experience in web design and development, including WordPress, Shopify, Google Blogger, Weebly, Custom HTML-PHP Websites, Bootstrap, CSS, HTML, javascript, and jquery. I can create or customize websites. I can write, edit or modify coding as per your requirements.
Looking forward to hearing from you.
Thanks