How can I hide some fields from the frontend pages in Request a Quote?

You can disable sensitive fields such name, phone, email etc. from the frontend.
1- Login to WordPress Dashboard
2- Go to Quote settings > Settings > Entities tab > Quotes
3- Under Attributes section, disable the one you do not want to display to public. Options available for each field are:
Enable: Display this attribute on everywhere
Disable: Remove this attribute from everywhere
Show only in Admin: This attribute is still enabled on admin area. If you want to hide this attribute on the frontend forms go to Forms tab.