What tools do editors use to find and delete the worst types of new pages (spam, vandalism, and personal attacks)?
Huggle is one of the main tools that people use on ptwikipedia for RC patrolling. Also RTRC, FastButtons (https://pt.wikipedia.org/wiki/MediaWiki:Gadget-fastbuttons.js). There may be others.
Is there a common way that deletion reasons are recorded in the log? For example, in English Wikipedia, they include names for each deletion reason in the log (e.g "WP:CSD#G11" means the article was deleted as "spam").
Yes, Deletereason-dropdown is commonly used: https://pt.wikipedia.org/wiki/MediaWiki:Deletereason-dropdown.
This includes the formal reasons for speedy deletion: https://pt.wikipedia.org/wiki/Wikipédia:Eliminação_rápida#Regras_formais
These include a one letter prefix indicating namespace (with some execptions): A (Article namespace), C (Category mainspace), D (Discussion or talk mainspace), U (User namespace), P (Predefinition or template namespace), R (redirect) and G (technical deletion). There are also legacy rules that may still be used in some cases, these are indicated with "ER" the number of the rule.
The numbers indicate the reason. I translate here the relevant ones:
A1 - Article with gibberish title
A2 - Article with no context
A3 - Article with no content
A4 - Article with no statement regarding notability (people, animals, organizations, web content, events)
A5 - Article with no statement regarding notability (music, books)
A6 - Duplicated content
ER3 - Absurd titles, content moved to another article
ER4 - Absurd titles in an encyclpedia, content moved to another article
ER5 - Recurring content (same content as previously deleted)
ER6 - Spam, publicity, or pamphlet
ER13 - Copyright violations
ER20 - Unsuitable content