Choosing Between k-means, DBSCAN and GMM

For each of the following datasets, choose the most appropriate clustering algorithm from {k-means, agglomerative (Ward), DBSCAN, Gaussian mixture} and justify it in a few sentences. Also state the preprocessing you would insist on.

1. GPS check-in coordinates for a city: dense downtown, sparse suburbs, and 3 % of points are GPS glitches far out at sea. You do not know how many "hotspots" there are.
2. Twelve standardised customer metrics for 2 million customers; marketing needs exactly 5 actionable segments and wants a membership confidence for each customer so ambiguous ones can be excluded.
3. Pairwise sequence-similarity scores for 800 protein sequences (you only have the distance matrix, not feature vectors), and biologists want to see the nested grouping structure.