With regard to numbering of locants, the principal characteristic group (the characteristic group chosen for citation at the end of a name by means of a suffix or a class name, or implied by a trivial name, e.g. propanoic acid) has seniority over simple substituent groups (e.g. chloro). On this matter, the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:
P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(…)
Note that Rule c takes precedence over Rule f.
Therefore, the preferred IUPAC name for the given structure is 3,3-dichloropropanoic acid (not 1,1-dichloro-3-propanoic acid).

As you have correctly assumed, additional chloro substituents increase the acidity of the carboxylic acid due to their electron-withdrawing inductive effect (−I effect):
acetic acid: $\mathrm{p}K_\mathrm{a} = 4.756$
2-chloroacetic acid: $\mathrm{p}K_\mathrm{a} = 2.87$
2,2-dichloroacetic acid: $\mathrm{p}K_\mathrm{a} = 1.35$
2,2,2-trichloroacetic acid: $\mathrm{p}K_\mathrm{a} = 0.66$
The acidity of chlorocarboxylic acids is hardly directly affected by the length of the carbon chain:
2-chloroacetic acid: $\mathrm{p}K_\mathrm{a} = 2.87$
2-chloropropanoic acid: $\mathrm{p}K_\mathrm{a} = 2.83$
2-chlorobutanoic acid: $\mathrm{p}K_\mathrm{a} = 2.86$
However, the effect decreases as the distance between the chloro substituent and the carboxyl group increases:
2-chloroacetic acid: $\mathrm{p}K_\mathrm{a} = 2.87$
3-chloropropanoic acid: $\mathrm{p}K_\mathrm{a} = 3.98$
4-chlorobutanoic acid: $\mathrm{p}K_\mathrm{a} = 4.52$
($\mathrm{p}K_\mathrm{a}$ values taken from “Dissociation Constants of Organic Acids and Bases”, in CRC Handbook of Chemistry and Physics, 90th Edition (CD-ROM Version 2010), David R. Lide, ed., CRC Press/Taylor and Francis, Boca Raton, FL.)
more -I effect
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