Installing Windows 10 on MacBook early 2008 without bootcamp - black screen blinking cursor
I assume you are trying to install a 64 bit version of Windows 10 because your processor is 64 bit. After Reviewing the web site Install Windows 7 and earlier on your Mac using Boot Camp, I found Apple documents only 32 bit versions of Windows 7, Vista or XP are designed to run on your Mac Book (2008).
The computer used to enter this answer is a 20&quot; mid 2007 iMac running 64 bit Windows 10 Pro. The same web site documents that my iMac can not run 64 bit versions of Windows, so this site can be wrong. On the other hand, just because I can do it does not mean you will be able.
The first thing I would check is the Mac's firmware. Current Apple firmware can be found at this site: About EFI and SMC firmware updates for Intel-based Mac computers.
Neither of our Macs can boot the Windows 10 installer from a USB flash drive. So, there is no point to trying that method to install Windows 10.
My iMac can not boot from a standard 64 bit Windows installation DVD. This is because these DVDs contain both the BIOS/MBR and EFI/GPT methods of booting. When you tried your DVD, the icon labeled &quot;Windows&quot; was the BIOS/MBR method and the icon labeled &quot;EFI&quot; was the EFI/GPT method. If you are having the same problem as me, you would have to remove the EFI/GPT method from the DVD. Unfortunately, this requires a machine running Windows. The procedure is given at “Select CD-ROM Boot Type:” error during Windows install.
The XP, Vista and Windows 7 32 bit DVDs only contain the BIOS/MBR method of booting. I assume this is also true for Windows 8, 8.1 and 10. If you can find a 32 DVD,  you could test to see if dual booting is your problem. You can download a free 90 day trial of 32 bit Windows 10 Enterprise at this site.
Another option will be to install VirtualBox on you Mac. Since you are using OS X 10.7, you would need to download and install the last version 4.3 release of VirtualBox. This would allow you to test the DVD by booting from the DVD in a Virtual environment. You could also install Window 10 in the virtual environment, but I am afraid your Mac is to slow for this to be of any use. (If you do, be careful not to active the Windows 10. To be safe, maybe you should not be connected to the internet while using the virtual machine.)
You could use VirtualBox to just install Windows to Mac's Boot Camp partition  and then run a physical version of Windows 10 without the aid of VirtualBox. The difference between this method, and directly using the DVD, would be that you could remove the EFI files before booting the Windows 10 installer. The procedure would be a merger of the instructions given here and here.
I am sure I have not answered all you questions. Feel free to post comments with additional questions.
BTW, the partition tables you added to your question look good. The output from the command gpt shows the GUID Partition Table (GPT) used by OS X. The command fdisk shows the legacy Master Boot Record (MBR) partition table that will be used by Windows. The first entry in both tables is the (hidden) EFI partition. This partition always starts at different values in the tables, but ends at the same value. The next three are your OS X, (hidden) OS X Recovery and Boot Camp partitions. The negative values appear to be a bug in fdisk. The values are suppose to be printed as unsigned values. What is shown are signed values. You can convert to the correct values by adding 2 to the 32nd power (i.e. 4294967296). In other words:
fdisk value                gpt value 
-1861551096 + 4294967296 = 2433416200
-1861141456 + 4294967296 = 2433825840
-1859870720 + 4294967296 = 2435096576