Well your information confirms that the disk has been successfully created with a gpt partition table as this is what fdisk sees.
Although fdisk cannot handled gpt partitions but modern kernels can. The most useful tool for gpt partitioning tool is still parted.
My guess is you would have created sda1 to house your root directory /. The sda2 could be your own /home with sda3 being the swap. You could delete this swap and recreate it no more than 1Gb as no Linux uses so much swap. Most are contented with 0.5Gb.
I could not identify cause of your current booting problem but you could boot up a Mint Live CD and restore Grub2 again as follow
Basically you mount sda1 and from the third command check if / & /boot are inisde that directory. If they are then you change root from the Mint CD Linux into the the version in sda1 and use its kernel to restore Grub in sda.
mount /dev/sda1 /mnt/sda1
grub-install --force /dev/sda
I have checked with Mint site and it uses Grub2 since version 8.
Grub2 must be restored by a Linux kernel. The above procedure is similar to Task K3 from the "Just Booting tips" in my signature.