Unfortunately, your existing /home and the ntfs partitions you could remove are in completely non-contiguous regions, so you cannot easily just combine the space. If I were you, I would switch to LVM piece-meal. Ideally, you’d have some other medium were you can temporarily store the current contents of /home while your repartition the drive. Then combine sda2 and sda7 into a volume group and pull just one logical volume out of it for the new /home.

Otherwise, create a new volume group with only sda2 in it (just overwrite the existing ntfs filesystem) using vgcreate, create a logical on top of that using lvcreate, make a filesystem in that using mkfs.ext4, I would add the -m 0 parameter for a non-root filesystem, mount that somewhere under /mnt/, move or copy over all the contents from /home to that mountpoint, taking care to replicate file owners and permissions (I would just use cp -a), then once this is done (and you’ve double-checked that it is because at the next step you can lose data if you’re not careful), umount /home, extend the volume group to include sda7 using vgextend, enlarge the logical volume for the new /home to the maximum using lvresize, enlarge the ext4 filesystem in there to the maximum possible using resize2fs, finally editing /etx/fstab to use that new logical volume as /home and remounting /home.

I wouldn’t want to put the air intakes of my Thinkpad directly on the grass like that. It’s bound to suck in dirt.