If I have had two partition on my laptop ever since I use Linux. One for root and another for home.
What does ubiquity do if I ask it to replace previous installation of Ubuntu with a new one? Will it install everything to / (root) or will it respect my partition scheme and take home partition as /home?
In my experience, upgrading or replacing my previous Ubuntu installation disregarded my previous partitioning method and built it's own (using ext4 of course).
I would go on the custom partition step, then select the partitions one by one (the size of the partitions are the same as the old installation), assign a filesystem, and check 'format' on each of them except swap space (if you have it). And remember to assign the correct device for boot-loader installation!
Hope this helps.
I would consider it a severe bug if it detected your old Ubuntu installation, offered to perform automatic actions based on that knowledge and then disregarded the mount points defined in /etc/fstab on the old system root. But I haven't tried it myself, so I can't tell you that it works. I would be extremely surprised if it didn't.
Ubiquity gives you a choice about what you want to do with your partitions. If you use manual partitioning, you can reuse your existing partition layout. This is what I do. I am able to reuse my existing /home as the /home partition for the new install. And I can choose to format that partition or not.
I have reused existing partition layouts on new Ubuntu installs several times with both Ext4 and btrfs filesystems. It works exactly as expected. No surprises and no problems (as long as you are familiar with partitioning, which it sounds like you are). Just use manual partitioning when you get to that step in Ubiquity.
On the other hand, if you are expecting it to automagically reuse your partitions with all the default installation choices, it will not do that. It will install everything to / (root).