Any idea why the icons are impinging on the text in the profile fields? 

This is a small CSS conflict with the theme or other plugins. We'll need some example URL to debug it.

And how to remove some of these social media fields, such as Yahoo, ICQ, etc?

Please read Robert's answer here: 

https://wpforo.com/community/how-to-and-troubleshooting-2/editing-profiles-social-media-fields-wp-discord-app/#post-18147

This is not accessible if your profile system is switched to BuddyPress. I mean this become accessible if you temporarily switch to the value of the Profile Page option in Dashboard > Forums > Settings > Features admin page. Once you switched it you can access to the forum profile system and forum profile account page: https://letslearnirish.com/forum/account/

https://wpforo.com/wp-content/uploads/2020/07/wpForo-Forum-Profile-URL-switcher.png

Here is yours in wpForo Community: https://wpforo.com/community/account/drumlinking/

There is no way to do that. There is no way to show wpForo avatar on the BuddyPress profile page. But the BuddyPress profile picture can be shown in forum posts if the user avatar is set "Defaut Avatar":

https://wpforo.com/wp-content/uploads/2020/07/2020-07-02_1956.png

Once you set it, go to Dashboard  >Forums > Dashboard admin page and click the button.

If you still have such issue, provide larger screenshots of the user forum profile page, BuddyPress profit page and a direct URL to some of them.

Please note: wpForo uses WordPress native (core) get_avatar() function. So if forum users don't have avatar on their forum account pages (i.e. there is set option "Default avatar"), in this case if the user upload an avatar on BuddyPress, the get_avatar() function will show the BuddyPress avatar on forum pages. This works fine on all our test websites.  

In your case this may be a cache issue, so please delete all caches and check again. Also, please check and make sure on other pages (none forum) the avatar for the current user is the same as he/she uploads on BuddyPress.