There are only two ways to be sure of your goggles. Buy a lpm and test them yourself. Or buy a certified pair.
If your laser is dpss you will also need goggles that have ir protection.
In a open field as long as you don't shine it on anything reflective or close to yourself you will probably be OK but I don't recommend this unless you are very familiar with lasers and confident in your ability to operate it in a safe manner and keep it pointed in safe direction at all times.
Always use google indoors especially when burning.
You will be able to see the dot, yes, especially if your laser is actually 100mW. I don't know about the 405, as I do not currently have a working 405nm laser to test it with. I just tried it with 75mW of 532nm and the dot is clearly visible.