What is the formula of a compound formed by combining Fe+3 and HCO3-1?

Fe (HCO3)3

Also, you would expect Ca(OH)2 to be soluble in water, due to it's high ionization potential.

There isn't one.  Fe(HCO3)3 does not exist.  The reason is that solutions of Fe3+ are too acidic for the carbonate or bicarbonate ion.  They will react and form CO2 gas.

Ca(OH)2 is not very soluble in water at all.  The Ksp for Ca(OH)2 is 7.9 x 10^-6.  Soluble hydroxides will have Ksp values much greater than 1, as in the 100's or 1000's, for instance.  The only really soluble metal hydroxides are those of the group IA metals.

Don't confuse the low solubility of Ca(OH)2 with Ca(OH)2 being classified as a strong base.  Being "strong" or "weak" has to do with the degree of dissociation.  Ca(OH)2 is classified as a strong base because what little Ca(OH)2 that does dissolve in water will dissociate completely.

============= Follow up ==============

Perhaps this is a typo:  "Fe3(HCO3)3", but it doesn't exist either.  But let me say again.  There are NO compounds of either a carbonate or a bicarbonate and iron(III).  They do not exist.  You will find them nowhere in the Handbook of Chemistry and Physics.

As for Ca(OH)2 being soluble in water, we've seen the low value of Ksp, but let's put it another way.  The solubility at 25C is about 1.5 g per 1000 mL.   This is why the solubility rules will sometimes say that calcium, strontium and barium hydroxides are slightly soluble.  There is no clearly defined definition for "slightly soluble".

Fe3(HCO3)3

Ca(OH)2 is is slightly soluble along with Sr)OH)2
All hydroxides are insoluble,except  the Alkali metals.barium and ammonium.
The solubility increases as you go done in group IIA.  Mg(OH)2 dissolves in excess waterLimewater, Ca(OH)2 is soluble and forms a clear solution  and is a good test for the gas CO2 which turns it milky as it forms Ca(HCO3)2