Hello there,
Thanks for writing in!

We are very sorry for the late answer, we were working with a limited resources for a past few days, thank you for your patience and your understanding!

The size of the photos really depends on the section that photo is uploaded to, so you should decide which is the biggest physical dimension on the live site of the photo you want to see, and do not upload bigger photo that that size(besides the logo which should be uploaded 2x bigger).

For example optimal size for full screen sections is 1920pxx1080px.

Here are some general tips for speeding up your website:

a. Consider optimizing your images with some tool like this one:
www.jpegmini.com

b.  Also you can install some plugin for cache, like WP Fastest Cache or some other:
https://wordpress.org/plugins/wp-fastest-cache/
https://wordpress.org/plugins/wp-super-cache/
https://wordpress.org/plugins/w3-total-cache/
c. Enable gzip compression on your server. You can read more about it here:
http://www.feedthebot.com/pagespeed/enable-compression.html

But it comes down to pasting this code to .htaccess file located in your folder:

<ifModule mod_gzip.c>mod_gzip_on Yes
mod_gzip_dechunk Yes
mod_gzip_item_include file .(html?|txt|css|js|php|pl)$
mod_gzip_item_include handler ^cgi-script$
mod_gzip_item_include mime ^text/.*
mod_gzip_item_include mime ^application/x-javascript.*
mod_gzip_item_exclude mime ^image/.*
mod_gzip_item_exclude rspheader ^Content-Encoding:.*gzip.*
</ifModule>

d. Also check - Leverage browser caching:
http://www.feedthebot.com/pagespeed/leverage-browser-caching.html

e. Use at least PHP 5.6.x or greater in order to process PHP code faster.

Please let us know if there is something else we can do for you!
Thank You,
Norah