Loaded your save. Your food problem comes from: 

1) Slow gamespeed setting. I'm not a Vodyani player, but I've heard that on slower speeds they indeed tend to die of starvation, because of... reasons.

2) Manpower situation. When you build or buy a ship (Ark included), it spawns with 0 crew. Then it will replenish its crew from your manpower reserve. 40 men for scouts, 100 for normal ships (like the one you bought), 220 for arks. Your manpower reserves will in turn replenish themselves consuming quite a bit of your food production.  It will pass.

3) You haven't activated population luxury boost. It would cost you 4 superspuds per 10 turns and would drastically boost your outputs, food included. From your save I activated the boost, bought a few ships to waste manpower, and upgraded main sustem to 3rd population - it was still positive on food. Without the boost it's negative while replenishing manpower, positive otherwise. Unluckily for you, you didnt spawn with boost resource (which is choosen at random), but anyway you've found 5 of it somewhere, futhermore you could buy it from the marketplace, there is ~100 available

4) Idk at which point you recognized your food deficit, but it was questionable decision to choose Transvine as system upgrade resource, while having access to RedSang. RedSang upgrade would give you + 60 food production, that would solve all your food problems outright. Yes, transvine gives food thru happinnes, but it is easier to access by other means, e.g. 'toys for boys' law. Other faction, other situation I would probably choose Transvine too, but not when I'm about to get into starvation quagmire.

5) Ironically, one of the causes is you unlocking 3rd (Ash) planet on home system. It added additional consumption, while offering little food production :D Net effect would be minus ~10 food with luxury boost.

Also, general remarks on your build.

1) Do not build wonder. Well, not in such situation anyway.

2) You didnt redesign your starting ark. On turn 1 remove ALL modules and place 3x All Shall Serve (Production module) or 2x production + 1x science. Probably the latter, I'm not quite sure. That should cost 60 dust. Try reloading a few times to figure out how to fit 1st turn redesigns into your starting dust stock. At some point later I prefer adding or swapping into influence modules, to contest minor factions.

3) 1st turn Hero refit - add 2 engines, no probes. Remove all defence and some guns to minimise the cost. Note that your hero still has +2 engine while you have +3 engine aveliable from the start. Scouts refit - replace collector module with engine. Also there's an option of refitting 1 leecher into 4x engine - it will give 16 movement for scouting. But you won't have dust to do it ALL 1st turn. Essence farming is not really that important that early.

4) You have too few ships for my taste. I prefer spamming ships from the start, my take on Vodyani is that it is rather agressive faction, bcs of decent scout ships, +1 speed and religious law. Especially if you play on Slow. On the 1st turn lay down a scout (probes+engine) with 1 beam (it's cheaper) or without any guns. The idea is to launch it on turn 3 (normal speed, ark refit into 3x production) with Military law (cheaper fleets). Speaking of laws, I prefer turn 1 science from scrap, and turn 2 (turn 4 on slow?) - cheaper fleets. Again, need to adjust it to game speed, by calculating production. 

5) Having build 1st, underarmed, scout, I prefer spamming 4 more fully armed scouts, those are for killing quest pirates (btw you didnt complete trivial 1st quest by turn 50), for killing normal pirates, for guarding leechers, for... scouting, for curiosities and for opportunistic agression on other (AI) empires. You have religious pinned law - might get some value out of it. 1st turn I attach hero (now disarmed) to starting scout, mess around till 1st fully armed scout finishes, then rearm hero, take hero +2-3 scouts and go adventuring. That fleet will kill anything you might encounter in near future, and maybe even capture some 1 pop enemy system :D There will also be a few independent scouts for other directions and for replacing wounded scouts in hero fleet. The point of mass-scouts is that you can both make an "assault" force with hero and have extra scouts for just scouting.

6) As for pirates - at some point you'll want to actually destroy their base. For that you'll need fleet that has 2/3 manpower of target base (iirc 1st level base is 300 defenders). Also by that time you should upgrade your infartry (military screen). Or even get tank tech (Autonomous Construction). Raw scouts probably won't do, you'll need either manpower module (Ubiqitous surveiliance tech) or proper combat ships (carrying 100 crew each). For normal pirate difficulty 1 scout with 1 manpower module + 2 regular combat scouts will be probably enough. As for combat ships, I'm not sure what's better - to build your own (unlocking designs + 1 mil tech) or to buy them (unlocking merc market). Guess market is better. That's not just for pirates anyway - it's good to have some ships for opportunistic agression here and there or just for defence. 

7) Battle tactics - you have acces to "take trophies" tactic, should add it on turn 1, perhaps instead of turtle. 30 dust and 10 science per destroyed ship (e.g. pirates) is very good earlygame. You'll have to destroy 4 ships as per your quest anyway.

8) So I my "build order" is to spam 5 scouts total (+1 starting one), then all buildings, then combat ships or whatever.

9) As for techs - didn't figure it out yet. My take is as follows:

- If ark refit 2prod 1 science then 1) Ubiqitous surveiliance to unlock tier 2 military which gives improved weapon and protection modules. You'll refit you hero+2 scouts into them. 2) Unlock a planet in home system 3) Titanium tech for building 4) Baryotic shielding (free movement) 4) Hull designs 5) Market techs

- If ark refit 3 prod (i prefer that) then skip surveiliance and just go planet-titanium-baryotic- market. You'll have to do with just basic scouts till merks appear.