The Hebrew Date Converter REST API already supports this.

https://www.hebcal.com/home/219/hebrew-date-converter-rest-api

For example, if you use this URL

http://www.hebcal.com/converter/?cfg=json&hy=5749&hm=Kislev&hd=25&h2g=1

You will get this response:

{"gy": 1988,"gm": 12,"gd": 4,"hy": 5749,"hm": "Kislev","hd": 25,"hebrew": "כ״ה בְּכִסְלֵו תשמ״ט","events": ["Parashat Miketz","Chanukah: 2 Candles"]}

Notice that the Parashat haShavuah is contained in the events array.

We typically light candles 18 minutes before sunset in most of the world, but 40 minutes before sunset in Jerusalem.

When you specify Jerusalem using the typical URL in Hebcal, you get the special 40-minutes-before-sundown feature automatically.

If you are going to specify candle-lighting times with our API by latitude, longitude and time zone and you want to specify 40 minutes before sundown for Jerusalem, be sure to specify b=40 in the URL (overriding the default b=18).

Yes, you can use the Jewish calendar REST API to get only parashat haShavuah for an entire year like this:

http://www.hebcal.com/hebcal/?v=1&cfg=json&s=on&maj=off&min=off&mod=off&nx=off&year=now&month=x&ss=off&mf=off

The s=on means Parashat haShavuah. The other features (major holidays, minor holidays, etc) are all set to "off"

We hope to release a feature in the future to allow uploading a CSV file to the Yahrzeit calculator. In the meantime you can use this link to enter up to 20 names

https://www.hebcal.com/yahrzeit/?count=20

https://www.hebcal.com/home/50/what-is-the-triennial-torah-reading-cycle

We've added support for candle-lighting times to our Jewish Holiday REST API. For example:

http://www.hebcal.com/hebcal/?v=1;maj=on;min=on;i=off;lg=s;c=on;year=2015;month=12;geo=geoname;geonameid=2988507;cfg=json

More documentation on that API is here:

https://www.hebcal.com/home/195/jewish-calendar-rest-api

Pesach 5776 begins on Fri, 22 April 2016 at sundown (15th of Nisan, 5776)

{
  "link": "http:\/\/www.hebcal.com\/sedrot\/reeh",
  "leyning": {
    "1": "Deuteronomy 11:26 - 12:10",
    "2": "Deuteronomy 12:11 - 12:28",
    "3": "Deuteronomy 12:29 - 13:19",
    "4": "Deuteronomy 14:1 - 14:21",
    "5": "Deuteronomy 14:22 - 14:29",
    "6": "Deuteronomy 15:1 - 15:18",
    "7": "Deuteronomy 15:19 - 16:17",
    "torah": "Deuteronomy 11:26 - 16:17",
    "haftarah": "Isaiah 66:1 - 66:24 | Shabbat Rosh Chodesh",
    "triennial": {
      "1": "Deuteronomy 12:29 - 13:1",
      "2": "Deuteronomy 13:2 - 13:6",
      "3": "Deuteronomy 13:7 - 13:12",
      "4": "Deuteronomy 13:13 - 13:19",
      "5": "Deuteronomy 14:1 - 14:8",
      "6": "Deuteronomy 14:9 - 14:21",
      "7": "Deuteronomy 14:22 - 14:29",
      "maftir": "Numbers 28:9 - 28:15 | Shabbat Rosh Chodesh"
    },
    "maftir": "Numbers 28:9 - 28:15 | Shabbat Rosh Chodesh"
  },
  "date": "2015-08-15",
  "hebrew": "\u05e4\u05e8\u05e9\u05ea \u05e8\u05d0\u05d4",
  "title": "Parashat Re'eh",
  "category": "parashat"
}