[RedDevil]

What tire pressure you can use depends om any things. In my car I found a higher pressure made for a better ride, especially improving cornering and reducing side wind sensitivity. I'd raise it for that alone.

The max sidewall rating is way below what the tire can handle, but in your case I would not go beyond that. The biggest gains are in the bottom end; 30 to 35 has a big effect, 40 to 45 much less so.
44 is already 14 PSI above vehicle recommendation.
Better play it safe and take small steps, and keep track of the handling at every step.

Good quality tires pay themselves back over time, not just in economy but improved grip, batter handling, maybe even less punctures.

Alloy rims usually have big gaps between the spokes causing more drag than steelies; it is easy to mount aerodynamic hubcaps on steelies to further reduce air resistance. If you do a lot of highway that may tip the scale despite the weight.