Why are there both stop and start codons?
Start and stop codons are instructions for the ribosome to start and stop protein synthesis, respectively.

The region between the start and stop codon (inclusive of them) is called ORF (open reading frame) or sometimes CDS (Coding sequence). 

Why does ribosome need explicit instructions for start and stop?

Ribosome recognizes an RNA as a mRNA if it has certain features. In bacteria and other prokaryotes there is a region on the mRNA called the Ribosome Binding Site (RBS) that helps in initial recruitment of the ribosome. In eukaryotes there are Kozak consensus sequences that help in identification of a start site. When the ribosome encounters an AUG codon then the initiation reactions take place (there are some proteins called initiation factors that help in this process). The ribosome just keeps moving along the mRNA and producing a polypeptide unless it encounters a stop codon. When it does other proteins called release factors come into play and they dislodge the ribosome from the mRNA. 

What about a second AUG codon?

If the ribosome encounters another AUG codon after the start then it would consider it as a codon for methionine. However there are situations when the second AUG can act as an alternative start site. You can see this paper for details. 

Why is stop codon essential?

You can imagine a situation where ribosome just goes till the end of mRNA — why stop it? The reason for this is that the mRNA 3' terminus usually has regulatory regions and most importantly poly-A tails (in eukaryotes) that should not be translated. Moreover stop codon also signals the ribosome to dislodge from the mRNA. If such processes didn't exist then ribosome will remain attached to the RNA.

If I only had a stop codon, would that also imply the next codon was start?

No. Because stop codon works only when translation has already started. However it is not essential that the stop codon should be followed by the 3'UTR. Usually in bacteria a single mRNA codes for multiple proteins. There are many ORFs that are lined one after the other; such mRNAs are called polycistronic mRNAs. In these cases there is another start codon a few distance ahead of a previous stop codon.