Use Ubuntu laptop as a Wi-Fi repeater

For Ubuntu 14.04, there is the option right in the connect menu. Click on the Wi-Fi icon at the top-right corner of your screen and then click on the Create new Wi-Fi network. It opens the dialog box, where you can give it the name, protection method and password. So there is no need to install any other package like Connectify.

And as for the second question, it will be more complicated. If it doesn't work automatically, then you should edit some Wi-Fi settings through dconf-editor. Better to ask experienced users at askubuntu. Hope it helps.

You can do that from the terminal. But first your laptop's network card must support AP (access point). Check out this question on ubuntu forum how to do that. Also you will find there how to set it up. But in case you want to share the connection from the same card you are connected with the other windows laptop, that can be done only with some cards only. Check out this question (as mentioned on one of the comments above too).
Now, if that doesn't work, I would recommend another way... Try using the ubuntu laptop to share the internet, and the windows one as a "repeater". Some people say it works (as I never tried myself), using this tool from microsoft. If that doesn't work too, than the only way it to use two different wireless cards on the ubuntu laptop, or to connect both laptops with a LAN cable (sharing the internet through the cable), and with the ubuntu laptop share the connection via wireless.

Now for the second question... I'm not sure if I got it right, but is that proxy configured in the router? If so, here is some help on how to configure browsers on Squid. And if you want to configure a wireless connection to use proxy from your windows phone, check this tutorial.
Now if you want to create a proxy server based on Squid, so that windows phone can connect to, I'm not quite sure how you can do that on ubuntu, but as for windows is pretty similar as a normal proxy server. Check this tutorial for that.

P.S.
In case I was off point somewhere or I didn't understood the question properly, please let me know, so maybe I can help you farther.