Yes. This long-known variation in strength as a function of load angle is recognized in  AISC Specification Section J2.4. The maximum strength increase permitted therein is 50 percent, which occurs for a load perpendicular to the fillet weld. The strength increase comes with a trade off; the weld has less deformation capacity in the transverse direction. When the load angle is intermediate between longitudinal and transverse, the strength increase will vary between none and 50 percent, respectively. There are restrictions. When fillet welds are used in groups with elements in different directions; strain compatibility has to be considered. One way to do that is to use the Instantaneous Center of Rotation Method as described in Part 8 of the AISC Steel Construction Manual. The Specification recently prohibited the increased strength in fillet welds subject to tension around the perimeter ends of square and rectangular HSS members.

No. As long as a matching electrode strength is used (see also FAQ 8.7.5) the strength calculated based on the weld throat will be more critical than the fusion zone (base metal) at the weld leg.

Acceptable and unacceptable weld profiles are specified in AWS D1.1/D1.1M Section 7.23. Such profiles are subject to misinterpretation when a fillet weld has been inadvertently oversized. AISC recommends that either or both legs of fillet welds may be oversized without correction, provided the excess weld metal does not interfere with the satisfactory end use of the member. Attempts to remove such excess weld metal may cause shrinkage, distortion, and/or cracking. The profile of fillet welds shall be in accordance with AWS D1.1/D1.1M Section 7.23.1.

From AWS D1.1/D1.1M Table 8.1, A fillet weld shall be permitted to underrun the nominal fillet weld size specified by 1/16 for 3/16, by 3/32 for 1/4, and by 1/8 for welds equal to or greater than 5/16 in. without correction, provided that the undersize portion of the weld does not exceed 10% of the length of the weld. If this limit is exceeded, additional weld metal can be deposited on top of the deficient area to increase the size as required. Web to flange welds of girders cannot be undersized at each end for a length equal to twice the flange width.

This topic is thoroughly covered in  AISC Specification Section J2.2b and corresponding Commentary.

The Commentary to Section J2.2b of the 2016 AISC Specification explains the reason: “For thicker members in lap joints, it is possible for the welder to melt away the upper corner, resulting in a weld that appears to be full size but actually lacks the required weld throat dimension. See Figure C-J2.1(a). On thinner members, the full weld throat is likely to be achieved, even if the edge is melted away. Accordingly, when the plate is 1/4 in. (6 mm) or thicker, the maximum fillet weld size is 1/16 in. (2 mm) less than the plate thickness, t, which is sufficient to ensure that the edge remains. See Figure C-J2.1(b).

Generally, no. The weld all around symbol can be a dangerously simple tool that can cause excessive work. Up until 2015, tying welds out-of-plane was prohibited and that would often effectively prohibit the use of the weld all around symbol. That prohibition was deleted, but replaced with a caution. It was deleted to permit seal welds such as those required for galvanizing welded assemblies. The cautions added to AWS D1.1/D1.1M address the propensity for melting notches in the corners of elements and hiding bad fit. So, while tying around out-of-plane corners is no longer prohibited it is still discouraged. Also, welding all around entails welding on short edges and around fillets and other contours that can be difficult and is rarely needed. It is much preferred to define the joints that need to be welded. That can be done with symbols or with sketches.

From AWS D1.1:D1.1M Section 7.21.1, a root opening not exceeding 1/16 in. is permitted without modification. A root opening not exceeding 3/16 in. is generally permitted therein if the weld size is increased by the amount of the root opening or it is demonstrated that the required effective throat has been obtained. For plate thicknesses greater than or equal to 3 in., a 5/16-in. root opening is permitted if suitable backing is used.