I-Tec 150 Watt Power Inverter

Can I safely plug my laptop into this?

Generally, if a device uses a ‘wall wart’ it isn’t fussy about how clean the power is - what mainly matters is the amperage (watts) being adequate. If it doesn’t use a wall wart you should avoid things like this.

Yes.

“What’s hammer shaped and controls electricity?”

Did I just sense a Secret of Mana reference there? What’s == Watt’s?