Translation is a process by which polypeptides are synthesized from a mRNA transcript, which was previously synthesized from the process of transcription. During this process, tRNA acts as a carrier by bringing with it specific amino acids to the ribosome, which are then incorporated into a growing polypeptide chain.

Eukaryotic translation differs in quite a few ways from prokaryotic translation. For one thing, prokaryotic mRNA contains a Shine-Delgarno sequence, which serves as a binding site for prokaryotic ribosomes to assemble on the mRNA. This binding, in turn, helps to initiate translation in prokaryotic cells. Eukaryotic cells do not contain a Shine-Delgarno sequence.

Furthermore, in eukaryotes, translation always begins with the assembly of ribosomal subunits on mRNA in the cytosol. Therefore, translation always begins on free ribosomes in the cytosol! Sometimes, translation will also finish on free ribosomes if the resulting protein is destined to stay within the cytosol where it will serve its function. Alternatively, if the first few amino acids of the polypeptide consists of a specific "signal sequence," translation will be temporarily paused. During this time, the entire ribosome-mRNA-polypeptide complex will be translocated to the rough endoplasmic reticulum. Once attached, polypeptide synthesis will resume and the polypeptide will thread its way into the endoplasmic reticulum. As it does so, additional folding and post-translational modifications are usually done to the polypeptide for it to carry out its proper function. Generally, polypeptides that make their way through the endoplasmic reticulum are destined either to be secreted out of the cell, or to become incorporated into the endomembrane system of the cell. And finally, as polypeptides are synthesized on a ribosome, whether it is free or bound, the amino terminus (aka N-terminus) side of the polypeptide is synthesized first and the carboxy terminus (aka C-terminus) is synthesized last.

Proteins undergo translation with the help of ribosomes, which can be found in either cytoplasm or on the rough endoplasmic reticulum (rough ER). Proteins synthesized on the ribosomes in cytoplasm are destined for somewhere inside the cell. On the other hand, proteins synthesized on the rough ER are processed in the ER and Golgi apparatus and are transported to the membrane or the extracellular matrix. Since the protein in the question is found on a membrane, it must have been synthesized on the ribosomes on the rough ER.  

Recall that all three types of RNA are used in translation. mRNA is the template strand used to synthesize the protein molecule. It contains the information regarding the sequence of amino acids in the protein molecule. tRNA is involved in transporting the amino acid to the growing polypeptide chain. rRNA molecules make up the ribosomes, the location of translation.

Polymerase enzymes are used in DNA replication (DNA polymerase) and transcription (RNA polymerase). They are not involved in translation.

Translation begins when a start codon is recognized in the mRNA molecule. The start codon is AUG, which codes for the amino acid methionine; therefore, all proteins begin with methionine. There are multiple stop codons; therefore, the ending of proteins could be different from one another.

Note that the question is asking about the state of a protein molecule after the completion of translation. A protein can undergo further processing events in the rough ER and Golgi apparatus during which the starting methionine may be cleaved; therefore, the ultimate end product of proteins might have a different starting amino acid.

Like transcription, there are slight differences between prokaryotic and eukaryotic translation. In prokaryotes transcription and translation are coupled and occur in the cytoplasm. Recall that in eukaryotes, translation can occur either in the cytoplasm or on the rough ER. Membrane and secretory proteins are synthesized in ribosomes on the rough ER whereas the cytosolic proteins are synthesized in ribosomes in cytoplasm.

The start codon for both prokaryotic and eukaryotic translation is AUG. This codes for the amino acid methionine, which is usually the first amino acid added to a growing polypeptide chain.

As mentioned, coupling of transcription and translation only occurs in the prokaryotes. Eukaryotic transcription occurs in the nucleus and the products need to undergo post-transcriptional modification before entering the cytoplasm for translation; therefore, the two processes aren’t coupled in eukaryotes.

Every protein begins with methionine, therefore, this will be found in all proteins upon completion of translation. Recall that this methionine might be excised when the protein is further processed in eukaryotes.

5' AUG 3' is the start codon for polypeptide synthesis and corresponds to the amino acid methionine.

All nucleotide triplets can theoretically occur in translation. The genetic code is basically universal to all species, except for mitochondria, which create proteins independently from the cell. Each codon translates to an amino acid, a stop codon, or a start codon (which is also an amino acid, methionine). There are indeed 64 possible combinations of the nucleotides, by rules of combinatorics. The 5' terminal is written on the left, as a convention among biologists.

There are three tRNA binding sites -- A, P, and E (for Aminoacyl, Peptidyl, and Exit) -- but only one mRNA binding site. The enzyme which bonds amino acids carried by tRNAs at A and P is indeed called peptidyl transferase. tRNA is held at A and P when its anticodon matches the codon of the mRNA to be translated. Because each codon is three codons long, per amino acid, the mRNA is indeed shifted three nucleotides' length through the ribosome, each time an amino acid is added to the growing chain.

Among the amino acids, there are two which only have one codon that code for them: tryptophan (UGG), and methionine. Methionine, is, of course, special among them, because the same codon is also the start codon -- AUG. Aspartic acid, asparagine, tyrosine, and phenylalanine all each have two possible corresponding codons (respectively: GAC/GAU, AAC/AAU, UAC/UAU, and UUC/UUU).

eIF2B is a GEF (guanine nucleotide exchange factor) for eIF1 eIF2.