Because both beams are loaded in the transverse directions. No matter the magnitude, the transfer loads lead to moments. If you didn't assign the transverse loads, then check your model for geometric irregularities or input mistakes.
Understand the causes of errors in FEM programs:
See this articlefor more details.
A "bonded contact" is presumably the same as welding the parts together.
Presumably, the material also has non-zero Poisson's ratio.
A friction coefficient of 0.01 will allow the ends of the pin to expand radially as it is compressed. The small but non-zero friction coefficient will stop the compressed pin from being perfectly cylindrical as it ...
In structural analysis, the second-order effects ($P-\Delta$ or $P-\delta$) are obtained through the non-linear analysis, so in general, a structure consisted of slender members would require more iterations to converge.
depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use):
An iterative process starts:
A small increment of the load $\Delta F$ is applied (typically a percentage between 1% and 10%)
For those small load increments the displacements $\delta_i$ are ...