This is the new info for the first question you asked.
diskutil list
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *750.2 GB disk0
1: EFI EFI 209.7 MB disk0s1
2: Apple_HFS Macintosh HD 522.1 GB disk0s2
3: Apple_Boot Recovery HD 650.0 MB disk0s3
4: Microsoft Basic Data 227.2 GB disk0s4
diskutil cs list
No CoreStorage logical volume groups found
sudo gpt -vv -r show /dev/disk0
gpt show: /dev/disk0: mediasize=750156374016; sectorsize=512; blocks=1465149168
gpt show: /dev/disk0: Suspicious MBR at sector 0
gpt show: /dev/disk0: Pri GPT at sector 1
gpt show: /dev/disk0: Sec GPT at sector 1465149167
start size index contents
0 1 MBR
1 1 Pri GPT header
2 32 Pri GPT table
34 6
40 409600 1 GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
409640 1019700872 2 GPT part - 48465300-0000-11AA-AA11-00306543ECAC
1020110512 1269536 3 GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
1021380048 443766777 4 GPT part - EBD0A0A2-B9E5-4433-87C0-68B6B72699C7
1465146825 2310
1465149135 32 Sec GPT table
1465149167 1 Sec GPT header
sudo fdisk /dev/disk0
Disk: /dev/disk0 geometry: 91201/255/63 [1465149168 sectors]
Signature: 0xAA55
Starting Ending
#: id cyl hd sec - cyl hd sec [ start - size]
------------------------------------------------------------------------
1: EE 0 0 2 - 25 127 14 [ 1 - 409639] <Unknown ID>
2: AF 25 127 15 - 1023 254 63 [ 409640 - 1019700872] HFS+
3: AB 1023 254 63 - 1023 254 63 [1020110512 - 1269536] Darwin Boot
*4: 07 1023 254 63 - 1023 254 63 [1021380048 - 443766777] HPFS/QNX/AUX