Partitioning a new Dell XPS 15 L521X for Ubuntu

I don't know what you mean by /dev/sdb1 being "EFI." The Extensible Firmware Interface (EFI) is your firmware and is stored on an EEPROM on your motherboard, not on a disk (except for developer tools like DUET or the "firmware" used in virtual machines). The EFI does have an associated partition, the EFI System Partition (ESP), but it's a FAT32 partition that's normally 100-600MiB in size and that has a particular partition type code. Your /dev/sdb1 holds an unrecognized (that is, not FAT) filesystem, according to the GParted screen shot, and does not have the ESP type code, so it's not an ESP. Your /dev/sda1, OTOH, is an ESP; it's FAT32 and has its "boot flag" set (which is GParted's way of identifying the ESP type code).

To answer your bigger question, if you don't care about the Windows you've got on your computer or any of the other software or data that Dell has provided, you can delete all your partitions, on both /dev/sda and /dev/sdb, with the caveat that since I don't know what /dev/sdb1 is, I don't know if it might have some non-standard purpose for the firmware. (It's more likely that it's used by Windows, though.) When you install Ubuntu, it will create whatever partitions it requires, including a fresh ESP. (The existing ESP just holds the Windows boot loader and associated data, so deleting it shouldn't be a problem.) If you want to preserve your ability to install re-install Windows in the future, though, you should preserve /dev/sda6 and perhaps /dev/sda4. Alternatively, in the Windows 7 era, it was common for manufacturers to provide a utility to let you burn a set of DVD-Rs that would enable you to re-install Windows. You could look for such a tool in your current system and back up the relevant data in that way.

First: 20 GB should be enough for the root partition, at least if you put /tmp somewhere else and you don't intend to install large games system wide. 28-29 GB would be even better. /tmp is used for instance for temporary data when burning DVDs, so I recommend that one being bigger than 10 GB.

Second: The EFI partition does afaik only store data that has something to do with the installed operating systems, so if you want to get rid of Windows completely, it should be safe to remove it and (if you don't want to be forced to use BIOS emulation) to create a new one for Ubuntu (I'm not an EFI expert, so please don't blame me if this does not work - maybe you should make a backup of the whole SSD by dd'ing it to a file on an external HDD first?). According to the Ubuntu Wiki UEFI Guide, an EFI partition of 200 MB should be sufficient for Ubuntu, so by deleting the current one and creating a new one, you could get some more space for your root partition, yet it's not a necessary step, for Ubuntu can make use of a present Windows EFI partition as well. Afaik only Apple computers use the EFI partition for firmware updates (but as said I'm not an expert). One more thing: Some broken EFI firmwares don't allow you to install Ubuntu in EFI mode. If this applies to your notebook, you can simply use BIOS mode by booting the live DVD in BIOS mode.

On every computer I know, there exists no reason to keep any of the OEM partitions if one doesn't want to reinstall Windows without a Windows DVD.