I have 2 monitors (different sizes and resolutions) setup with the "Extended" monitor Win7 setup.

Problem 1

I can not "move" a window from my Primary Monitor (larger and higher resolution on right side in front of me) to my Secondary 2nd monitor (smaller and lower resolution) with just selecting the title bar with the left mouse button and dragging it to the left. Windows 7 "snaps" it back to the right Primary Monitor when the window is physically in the 2nd window area as I'm holding the left mouse button. I can prevent this problem - by holding down the Ctrl Key with the Left Mouse button, but this is extremely annoying to me.

Problem 2

I typically "lose" focus if I try typing input on the 2nd monitor. Typing is erratic with regard to keystroke accuracy from my keyboard translated into input on the 2nd screen. No problem with typing input on the primary left monitor.

I find this extremely annoying and turning off the "snap" feature via the Control panel does NOT work for me. Win7 stubbornly refuses to move my selected window to my 2nd monitor without me "forcing" Win7 to do this with the Cntrl Key.

I have tried various solutions including changing the resolutions of one or both of my monitors and sometimes "temporarily helps" but reverts back to the problem. Also if I swap the logical (not physical) layout so that I tell Win7 the monitors are setup in a reserved situation (Large monitor on the left, and small on the right) - this also sometimes helps for awhile - but is very awkward to work with "backwards". But all of these temporary solutions stop working. The only solution that consistently works for "moving" the screens is to hold the Cntrl Key down as I'm moving window with the left mouse selected on the title bar. Even that however, doesn't prevent the loss of typing focus for me on the 2nd monitor - while at the same time the typing on the 1st monitor is fine.

I have also tried the suggested shortcut - Windows Key + Shift, Left arrow Key (pressed together) or the same combo with The Right arrow Key - this doesn't move my windows at all (right or left). BTW - Win Key with "+" does engage the magnifier and maximizes my screen onto both monitors and I can restore the window with Win "-" fine.

Any help on moving my window screens from my Primary Monitor to my Secondary monitor without having to press the Ctrl key while holding down my left mouse button with be appreciated. Also any help on gaining typing "focus" into my 2nd screen with be helpful too.

You noted in the comments that you're using PowerPro. I am certain this is the cause of your troubles (and you confirmed this through your comments).

The PowerPro website notes that there is a version 4.9 available. This could possibly help with your issues. It may be worth a try.

In my personal opinion, the website of PowerPro does not look like it (or the software itself) is still well maintained. I would strongly advise you to look into alternative software.

Alternatives

Related: Multiple Monitor Software for Windows 7

Without knowing exactly what PowerPro provides to you, possibly a software like UltraMon (UltraMon costs US$39.95) is what you need.

Besides 3rd-party software. You already noted that you know about hotkeys in Windows 7 like Win+Shift+Left Arrow. In my opinion, a lot of valuable features regarding multi-monitor support were added in Windows 7 (like these hotkeys).