It depends on exactly which model it is. I have a model 1934 Mauser 7.65 pocket pistol that is worth (according to "the book") about $500, however, there are some rare models that are worth much more, some well over $1000, if I remember correctly.
100 or so
.32 caliber. In a semi auto handgun, probably .32 ACP
http://stevespages.com/ipb-remington-51.html
Value is too difficult to be accurate without seeing the gun. Condition which includes the amount of original finish and original configuration will determine value. Recommend taking it to a gun shop for appraisal.
50-300 depending on speicifics
Used good condition $200.00
value depends on overall condition and caliber............
Model 51 manual located here - http://stevespages.com/pdf/remington_51.pdf
150-300 USD or so
Which .45 handgun are you referring to? The .45 Colt revolver (Peacemaker) goes back to about 1873. The traditional "45 Auto" was adopted by the US Military in 1911, but there were other, earlier .45 caliber automatics. And of course, .45 caliber black powder ball and cap pistols, ball and cap revolvers, etc are MUCH earlier than the Peacemaker. So... which handgun?
Llama made both semi auto pistols and revolvers in .22 caliber. The pistol (Small Frame Auto) looks like a scaled down 1911A1 .45 Auto. There have been problems reported with the quality/hardness of steel, and greater wear than expected. Llama also made double action revolvers in .22 caliber. Value will depend on which model and condition, but may range from about $150-$300.
100-800